Put a comma after “specifically” when it starts a sentence. Also, use a comma before “specifically” when introducing a dependent clause; the comma after it is optional in these cases. Furthermore, do not use a comma when “specifically” is essential for the meaning of the sentence.

You would need a comma before “specifically” only if it was strongly connected to what comes after it, or if it provides additional information about something that you have mentioned before “specifically”. …

Use a comma after "in particular" or "particularly" at the start of a sentence to modify a clause. Do not use commas when modifying a single word.

Generally, there are two ways you can use the phrase “more specifically.” The first is to use it directly after a comma when you didn’t want to end the clause from before. The second is to start a new sentence with it. In these cases, you always need to include a comma after it to break up the sentence flow.