There is always a problem when combining the quotation marks with any other punctuation mark. The only thing to keep in mind is that every punctuation mark should be placed outside the quotation mark. Even the colon.

When you want to quote someone and using quotation marks, a colon is welcomed in the sentences instead of a comma symbol. This style is mostly used by writers and editors and it looks good on a paper.

E.g. writing dialogues between two characters in a play.

Take care when using this punctuation mark, in order to get the best result. As you can see, it has many purposes. But if you are also using a grammar app to check your papers and so on, it will tell you to use the colon only when you are creating a list. Otherwise, it will not let you use the punctuation mark for its purposes.