What should one do if they have not verified their purity for several years due to ignorance, then learned how to verify it? Should they fast a month for each year, or only the days they believe they were menstruating?

Doubt concerning the validity of an act of worship after completing it does not affect its soundness. Therefore, if a woman doubts the validity of her fast on certain days, the default is that it is valid. However, if she is certain that she fasted while menstruating, her fast is not valid, and she must make up those days. She is not required to make up any days other than those she fasted while menstruating. What she fasted after becoming pure is valid, even if she did not perform a proper ghusl, because ritual purity from menstruation is not a condition for the validity of fasting.