The single word “anytime” is a fairly recent addition to standard English. It should only be used as an adverb, and it would not be appropriate in formal writing.
The phrase “any time” can be used wherever “anytime” can be used, and in a lot of contexts where “anytime” cannot. The easiest path is to write it as two words. If you want to use “anytime” informally, I don’t think any mistakes you make using it will be obvious to most people, or judged harshly by those who do notice.
For your specific example,
Call me any time after 12pm.
is correct. If you wanted to use “anytime”, you would write:
Call me anytime, as long as it’s after 12pm.
This article on ThoughtCo has a lot more detail, and includes this helpful summary:
- "Any time" can function as either a noun phrase or an adverbial phrase.
- "Any time" is always correct.
- "Anytime" is always an adverb.
- "Anytime" cannot follow a preposition such as "at."
- Use "any time" when referring to an amount of time.
- Never use "anytime" in formal writing.