1. "I don't have any issues with the proposed schedule". (OK)
2. "I don't have any issue with the proposed schedule". (wrong)
3. "I don't have any issues on the proposed schedule". (wrong)
2. is wrong because "any" is normally used with plural or count nouns, and "issue" is a singular count noun. 3. is wrong because "issues" normally selects the preposition "with", not "on".