No comma after "But apparently" when it introduces a dependent clause:
* Example: "But apparently, the weather forecast is wrong."
In this case, "But apparently" is part of a dependent clause ("the weather forecast is wrong") and needs to be combined with it.
Comma after "But apparently" when it introduces an independent clause:
* Example: "I thought the game was over, but apparently it's still going on."
Here, "But apparently" is followed by an independent clause ("it's still going on"), making it necessary to separate the two clauses with a comma.
In summary:
* Use a comma after "But apparently" when it introduces an independent clause.
* Don't use a comma when it introduces a dependent clause.
Always consider the context and whether "But apparently" is followed by an independent or dependent clause.