Correct spelling, explanation: considering the history and origin of the language, the word apart has its roots in Latin as ad partem consisting of two elements ad and partem. Ad is a word-forming element expressing direction toward somewhere, used as a prefix. In Old French, it was simplified to a and this form has remained until today. The second element partem was also reduced and became part. Since the 14th century, the word has existed in English as apart. This is the reason why apart is correct, not appart.

Definition of apart:
adverb, when people or things are apart, they are far away from each other,
My boyfriend lives in Germany and I live in Poland. What a pity that we are apart!
They took him to prison and he and his wife were apart.

Phrases with apart:
joke apart – to speak seriously,
Listen, jokes apart. Why did you write this letter?
be worlds apart – when you say that two people or things are worlds apart you mean that they are very different from each other,
In my opinion, the novel is worlds apart from the movie.
rip someone/something apart – critisize; make a group of people argue and not united; destroy; make someone very sad,
One reviewer of this book ripped it apart but I still think that it’s really good.

Incorrect spelling, explanation: appart is an incorrect form of adverb consisting of two elements: the prefix a and the noun part. The additional p is not needed. As a result, appart is simply a misspelling, which also shows the origin of the word coming from Latin and then from Old French. The form apart with one p is solely correct.