これはおそらく戸籍上の出生年月日を調べた上で修正したのではないかと思います。

。

I think this was probably corrected after checking the date of birth on the family register.

Literal

This [topic-は] probably family-register-[on-上の] birth-date [obj-を] investigated [on-上で] corrected [nominalizer-の] [isn't-it-ではないか] [quotative-と] think [polite-ます].

戸籍上 'on the family register' uses the suffix 上 'on / in the context of' to scope the claim. ~た上で 'after doing X' is a formal conjunctive meaning 'having done X (and with that as a basis).' ~のではないかと思います is a hedged opinion construction — literally 'I think it might be the case that X' — a standard pattern for polite speculation in Japanese.