午前0-12 goes from 00:00 to 12:00 in 24h time. Do minutes affect 午前 / 午後? Is 12:30 in 24h time still 午前１２時３０分 or does it change to 午後 thanks to the minutes going over?
Legal Answer: 12:00 in 24h can be only written as 午前12時,
and therefore 12:30 in 24h might be 午前12時30分, because it's defined so by an ancient Japanese law (in 1872), which somehow seems to be still in effect. There is no such thing as officially-defined 午後0時. (EDIT: As @broccoriforest says, perhaps the more accurate way to describe this situation is: "Time notation between 12:00 and 13:00 has never been officially defined in the history of Japan"...)
Practical Answer: Forget the legal answer. 午前12時 itself is a confusing expression which should be avoided in most cases. Never say, for example, 午前12時30分 because it's very, very confusing. Let's not try to figure out its meaning seriously. Instead, always use 午前0時 (midnight) or 午後0時 (noon) which are unambiguous and used widely on TV, digital clocks, etc., and it I think is consistent with the common English clock system. 12:30 in 24h should be written as 午後0時30分, or 12時30分 without 午前 or 午後.
The most technically correct answer would be... both 午前１２時３０分 and 午後１２時３０分 are nonexistent. Because if you apply 12-hour notation rigidly, the time range only varies from 0:00 to 12:00 (whether the end is included or not is still debatable). Hence the value
12:30 a.m/p.m are simply not allowed.
That said, in daily life we could understand it by considering whether the time belongs to morning (= before noon) or afternoon. In this sense, 12:30 in 24-hour notation would be 午後１２時３０分, if you have to use the number 12:30.
As I see from your comment, your concern is related to the controversy about whether noon/midnight should have AM or PM. Basically it depends on definition, but at any rate, the ambiguity only involves the very moment 12:00 AM/PM. If the time should go past noon or midnight by a single tick, it'll automatically fall under either AM or PM.
In normal spoken japanese people often refer to 朝の１０時半 or 夜の２時, or something along that vein. (or just 今朝、or ２時から) 午後 or 午前 is quite formal but commonly heard in news broadcasts.