Moyahua Parish was created from Juchipila Parish in 1808. Parish records for Moyahua are available starting in 1813 (Padron), and baptism, death, and marriage records begin in 1814. Other areas to look for Moyahua families is in Juchipila, Mezquital del Oro, Cuxpala, Santa Rosa, and Apozol (Aposol) records. I also have found some Moyahua and Juchipila connections in Jalpa (Zacatecas). When Moyahua was split from Juchipila in 1808, some family territories were located in both Juchipila and Moyahua parishes, so it is possible to find families in both areas. It is located on several Nova Hispana maps dating back to 1636 under the name Moyauan.
The area known as Moyahua is very old, and in addition to the maps mentioned above, Moyahua is mentioned in various written records dating from the mid 1600's, and likely much further than what I have came across.
I am the admin of this website, but also a researcher of Juchipila parish and Juchipila provincia.
A recommendation with all genealogy is to find out what you can from your direct family, i.e. Mother-Father, Aunts-Uncles, Maternal-Paternal grandparents. This will likely establish a baseline of where you may need to focus your research.
When researching in Mexico, it is best to start out with Parish records, if possible. In 1860 Civil records became available, and these are also instrumental in researching Juchipila area families.
A listing of Juchipila Parish records and Juchipila Civil Records that are available are listed in the following link:
Besides the standard, Juchipila baptism, marriage, and death records, the 1844 confirmation records is a very good resource, with many older listed, some dating back to at least the 1780's. These records also provide parentage, due to parish record not being available in the 1700's and early-mide 1800's.
Juchipila.org - Volunteer Genealogy