It is important to clarify that the act of homosexuality (sodomy) during the fasting hours invalidates the fast, and the person must make up for that day. This is based on the consensus of scholars regarding the invalidation of fasting due to such acts.
As for having feelings or desires towards the same sex during the fasting period, this does not invalidate the fast. The fast is only invalidated by the actual act itself, not by feelings or thoughts. Therefore, if one repents after committing the act, they must still make up the fast for that day.
For further details, you may refer to the relevant religious texts and scholarly opinions.