You already accepted an answer but I am going to answer anyway.
Short Answer:
You either make your story a total fantasyworld, or if you want it to have even the slightest trace of sceientific plausibility you should ask for help from Sean Raymond at PLanetPlanet.
https://planetplanet.net/about/
Long Answer:
If the smaller world takes 700 years to orbit around the big planet, and the eclipse of the smaller world takes 100 years, the smaller world will be in the shadow of the larger world 1/7 or 0.1428571 of the total orbit.
Imagine that the larger world is totally spherical and the smaller world orbits around the center of the larger world in a cirular robit. And suppose that the shadow of the larger world will be a cylinder with a diameter equal to the diameter of the larger world.
If the smaller world orbits around the larger world right at the surface of the larger world, it will spend half of its orbit in the shadow of the larger world.
If the small world orbits the larger world with a radius from the center of the larger world equal to two radii of the larger world, the formula for the circumerence of a circle, 2 phi r, means that the orbit will have circumference of 12.5636 times the radius of the larger world. Thus the time spent in the shadow of the larger world would be 1/6.2818.
If you want the smaller world to spend 1/7 or 0.1428571 of its orbit in the shadow of the larger world, its orbit will have to have a circumference equal to 14 radii of the larger world. The smaller world will thus orbit 2.228171 planetary radii from the center of the larger world.
You didn't specify whether you wanted the smaller world and/or the larger world to be habitable for any liquid water using lifeforms in general, or for humans and beings with the same environmental requirements in particular. A naturally habitable world has to have become habitable over billions of years - it took Earth about 4 billion years to acquire a breathable atmosphere - which means that it should have had a stable orbit around a star for billions of years.
You also didn't specify whether you meant that the smaller world's orbital period around the larger world was its sidereal period or its synodic period.
Anyway, if the smaller world is a moon orbiting a planet orbiting a star, the moon should have have to have a stable orbit around the planet and the star for billions of years before the story if the moon is supposed to be naturally habitable.
And for a moon orbiting a planet orbiting a star to have a stable orbit for billions of years, the orbital period of the planet must be at least about 9, repeat nine, times as long as the orbital period of the moon around the planet. So the evil planet in the story should have an orbital period of at least about 6,300 years.
In order for the planet and moon to have temperatures suitable for liquid water using life, it should receive approximately as much radiation from its star as Earth gets from the Sun. Thus it should orbit the star near what I call the Earth Equivelent Distance or EED of that star.
The EED distance of a G2V type star like the Sun is obviously the distance of Earth's orbit around the Sun, or 1 Astronomical Unit or AU. The EED of a star in AUs is equal to the square root of the ratio of the luminosity of the star divided by the luminosity of the Sun.
A spectral type F0V star would have a mass of 1.60 Suns and a luminosity of 7.31 Suns. It would have a EED at 2.703 AU. According to this orbital period calculator it would have an orbital period in the EED of 3.513 years. F type stars spend about 2-6 billion years on the main sequence.
https://www.calctool.org/astrophysics/orbital-period
A spectral type A0V star would have a mass of 2.33 Suns and a luminosity of 38.37 Suns. It would have an EED at 6.1943 AU. The orbital period in the EED would be about 10.099 years. Vega, an A0V type star, is expected to spend only 1 billion years on the main sequence.
A spectral type B0V star would have mass of 17.70 Suns and a luminosity of 44,875 Suns. It would have an EED at about 211.8372 AU. The orbital period in the EED would be about 732.8 years. It would spend much less time on the main sequence than an A0V star.
A spectral type 03V star would have mass of 59 Suns and a luminosity of 660,693 Suns. It would have an EED at about 812.830 AU. The orbital period in the EED would be about 3,017 years. It would spend only a few million years on the main sequence.
A star with a planet in its EED can not last long enough for a moon of the planet to naturally become habitable if the planet has an orbital period of at least 6,300 Earth years.
Thus If your moon orbits a planet that has an orbital period of at least 6,300 Earth years, the moon would have to be terraformed by a superadvanced alien civilization.
And the planetary year could become long enough if the planet orbits far beyond the EED of its stars - which of course would require the moon to have another source of warmth.
Suppose the planet orbits a spectral type B0V star with a mass of 17.70 Suns and a luminosity of 44,875 Suns, and an EED at about 211.8372 AU. If the planet orbits at 1,059.186 AU it will have an orbital period of about 8,933 Earth years. If the planet orbits at 900 AU it will have an orbital period of 6,417 years.
You also have the problem that if a moon orbits its planet at a distance of 2.228171 planetary radii from the center of the planet it cannot have an orbital period of 700 years. Unless you make the planet very large but with a very low mass and density.
Suppose that a ficitonal planet has the mass of 1 Jupiter - 317.8 time the mass of Earth - and a radius of 10 jupiter radii. It will thus have the same mass as Jupiter in 1,000 times the volume, and will be only 0.001 times as dense as Jupiter. It will have a radius of 714,880 Kilometers and an orbit at 2.228171 planetary radii would be at a distance of 1,659,720 kilometers. A moon at that distance will have an orbital period of 0.03777 years.
Changing the mass of the planet to 1 Earth while leaving the size the same, the orbit of the moon (or twin planet) will have a period of 0.4768 years.
Changing the radius of the planet to 100 Jupiter Radii or 7,148,800, an orbit at 2.228171 radii will have a radius of 15,928748 kilometers. If the planet has 317.8 times the mass of Earth the orbital period of the moon will be 1.1229 Earth years.
Making the planet have 10 Jupiter radii but only 1 Earth mass, the orbit of the moon will have a period of 14.177 years.
So no moon can orbit its planet at a distance of 2.228171 planetary radii and have an orbital period 700 Earth years long unless the planet is a super low density ball of gas.
Hypothetically superadvanced aliens mentioned above could built a shell world of very great size and very low density.
Completely hollow shell worlds can also be created on a planetary or larger scale by contained gas alone, also called bubbleworlds, as long as the outward pressure from the contained gas balances the gravitational contraction of the entire structure, resulting in no net force on the shell. The scale is limited only by the mass of gas enclosed; the shell can be made of any mundane material. The shell can have an additional atmosphere on the outside.[1][6]
https://en.wikipedia.org/wiki/Shellworld
So maybe you should write your story as a fantasy set in a place which appears like a flat plain to the natives. There is a bright light in the sky which is lit for half of the time and unlit for the other half of the time.
There is a cycle of lighting which the mysterious light follows where the dark periods get longer relative to the light periods, and then the dark periods get shorter relative to the light periods. Such a cycle might take about 365 light/dark cycles to complete, or any other number you want, and might be considered to be the equivalent of a year by the natives.
And every 700 of those "years" the light goes dark and stays dark for 100 of what the natives call "years". Or you can use whatever numbers you decide on. And if you want, maybe the natives see a dark object move in front of the light object to hide it, and then move away to reveal the light source again.
If you want to make your story as scientifically plausible as you can, you should ask for help. An astrophysicist named Sean Raymond has a blog called PlanetPlanet about planets, many of them fictional and imaginary ones.
And he says he is willing to help with world building fictional solar systems. So maybe you should show him your question and my response and ask him to make it as plausible as possible.
https://planetplanet.net/about/