FTDNA/Family Finder

Is it a zero distance match?

Have they done Family Finder?

Yes it is. Also I and the other guy did the Family Finder

Do you match on Family Finder?

No. That's The pronlem.

About 10 percent of 3rd cousins do not share DNA (or not enough to qualify as a match).
Same for about 50 percent of 4th cousins
And same for increasingly large percentages of more distant relationships.

Seems you can conclude
You are related, but more distantly than 2nd cousin.

Do you have any siblings with Family Finder results?
Are there other relatives of yours on your father's side who have Family Finder results?

Unfortunately, there are no any men related to my father anymore. Only I and my brother and my son. Also to my disappointment, the match has passed away at the end of last year.

For Family Finder it does not need to be a man. That is the beauty of this.

There is almost certainly no advantage of more than one of you and your brothers and your father and his brothers, etc. doing Y-DNA Testing. You and they almost certainly have the same Y chromosome.
It is different with the autosomal chromosomes. And women get autosomal, not just men.

Have both you and your brother done Family Finder? If you have any sisters, have they done Family Finder?
Siblings do not get exactly the same bits of autosomal chromosomes -- there are likely many places where one may have a piece from your father's mother, another may have a piece from your father's father. So one may match this person while the other does not.

Thank you for your comprehensive explanation.

I have done also the Family Finder test. My sister made MH and my son FTDNA, But so far we have not found any close relatives, or matches, except that one with Y-111.

Your son only has the DNA on your father's side that he inherited from you. So that cannot add anything.

If your sister tested at MH after March 1, 2019, she can use the MH results to get FTDNA results free of charge.
- see https://www.familytreedna.com/autosomal-transfer
It is totally free to do so, and she can then, still at no charge, see all her matches at FTDNA (including total shared cM and longest segment, etc.).
(To use the Chromosome Browser and/or see ethnicity results, there is one onetime charge, $19)
More info: https://help.familytreedna.com/hc/en-us/articles/4402392808463-Auto...