Blocks filtering

Hello there!
We add each article in only one parent category but in several child categories that are not necessarily located under the same parent category.
We set as Primary Category, the one that suits as best, between the child categories.
We want to filter a block or a flex block in order to saw only the articles to have as primary category any of the child categories under a specific parent category. Is it possible?

For example, let’s say that we have:
“Parent-01” with Child Categories: “Child-01a”, “Child-01b”, “Child-01c” etc.
“Parent-02” with Child Categories: “Child-02a”, “Child-02b”, “Child-02c” etc.
“Parent-03” with Child Categories: “Child-03a”, “Child-03b”, “Child-03c” etc.

We upload articles by checking categories in the following way:
Categories: Parent-01, Child-01a, Child-01c, Child-02b, Child-03a
Primary Category: Child01a

We want to filter in a block, every article has as Primary Category one of the child categories “Child-01a”, “Child-01b”, “Child-01c” (under the same Parent-01 category), regardless of the additional child categories that may be included in this article, that aren’t located under the same Parent.

Thanks for your help

Thanks Vlad.

One additional question on this:

It is quite often to mark a post with more than one categories.
Is there any way that we could avoid repeating the same post again and again in different category blocks within the same page?

Thanks again.