Combine get_the_category and the_category

Does anyone know of a way to output only the children of a parent category, for a specific post, separated by commas? This would sort of combine get_the_category and the_category.

Say you have the following categories for the entire blog:

• Category A

• A.1
• A.2
• A.3

• Category B

• B.1
• B.2
• B.3

And a specific post belongs to only:

• Category A

• A.2
• A.3

• Category B

• B.1

I want to output hyperlinked child categories, separated by commas, for each parent category:

Category A: A.2, A.3
Category B: B.1

Ideally, I should also check whether this specific post belongs to any children of the parent category before writing “Category N: …”. So, if this post did not belong to any children of Category B, I would only output:

Category A: A.2, A.3