Are there any Jewish writings that suggest the Earth revolves around the sun and is not the center of the universe?
The Rebbe holds that both opinions are correct based on the theory of relativity by Albert Einstein.
This means there is a third opinion that supersedes the whole issue of heliocentrism and geocentrism, making both viewpoints equally valid, and the reason this is a relevant addition to answers focusing on what sefer may or may not have been written using heliocentric metaphor for ma'asah b'reshit.
(The Rambam wrote on ma'asah b'reshit, not on how to construct telescopes or otherwise create implements for the practice of physical science of the study of the stars, astronomy.)
This third opinion confirms the Earth is not the center of the universe, for no such thing as "a center of the universe" can exist.
My source is a shiur by Rabbi Y.Y. Jacobson, discussing both the the correct way of interpreting Maimonides' cosmology, how the theory of relativity supersedes both the Copernican heliocentric ("Western") and Ptolemaic geocentric ("Greek"/"Hellenistic") cosmologies.
More specifically, it answers the question of why this does not make the writings of Maimonides "obsolete" or "faulty", regardless of the relevancy of both geocentrism and of heliocentrism.
As such, it indicates that there is a possibility for Torah-true writings supporting heliocentrism to exist, and that you should ask your Rabbi which of the two hashkafos he holds to, preferentially before studying either of them.
The only parts of your answer I cannot answer is whether these texts have been written, whether they have been preserved and if so, where.
Three relevant starting points in the shiur:
I'm in the process of amending my answer to include Jewish sources that support heliocentrism.
Unfortunately, no - most Jewish sages until very recently insisted on the Sun rotating the Earth.
- The Talmud had some clear ideas of the sun circling outside a domed earth, moving through a window to the other side of the dome.
- Maimonides clearly describes the earth of being at a center around which the Moon, Sun, and the planets rotate.
- Rabbi Hayyim Vital writes about the earth being the center of "all of the worlds" like the pit of a date (עץ חיים שער א' ענף ד'):
נמצא כי כדור הארץ שאנו עומדים בו הנה הוא הנקודה האמצעית שבכל העולמות כולם כעין גרעין התמרה שהוא באמצע האוכל והאוכל מקיפו מכל צדדיו
- As recently as the 20th century, the last Chabad Rabbi insisted that the Earth actually rotates the Sun, and that this is compatible with modern science (which is technically partially true, but perhaps misleading)
Edit: The following article goes through a comprehensive list of sources from the 16th century onwards, showing that indeed no sources actually endorse the Copernican theory, with most rejecting it outright as blasphemy, up until the mid 19th century, with the Academic Rabbi Isaac Samuel Reggio supporting it.
*Though to prove this conclusively, we would need to go over every single source.
This answer is [only] a clarification of the previous answer:
There could be no authentic Jewish sources for claiming that the Earth rotates around the Sun other than ones that agree with the common science.
The reason is very simple - it has no practical Halachic implementations.
The only need to present the Solar system in its current form (Sun-centered) vs Earth-centered is to simplify the calculations of rotations of all other planets around the Sun. Technically, it is universally agreed that the physical Universe has no "center" and any point can be accepted as the center and the calculations made in accordance.
THe Jewish Halachah only uses 3 planets for all the practical laws: Earth, the Sun and the Moon. Even if we admit that the other planets (at least Venus, Mars and even Jupiter) were known in the ancient times, their rotation has no place in the Jewish Law and therefore the calculations are never mentioned.
NB: This dispute is similar to the dispute of calculating the orbits of space shuttles and satellites - whether Einstein's relativity must be used or Newton's laws work just fine. Turns out, most of the time Newton works just fine.
So a Sun-centered system presents no benefits whatsoever for calculating the Jewish times - daily, monthly or yearly.