Most Uralic speakers (Sami, Finns, Estonians, Udmurts, Mari, Komi, Nenets, Selkups, etc.) share a high percentage of Y-haplogroup N. The Hungarians are an exception. They have hardly any hg N (0.5%). Their paternal lineages are very typical of Central Europe (mix of R1a, R1b, I2a, I1, E1b, J2, J1, G2a). The only haplogroup that connects them to some other Uralic speakers is R1a, but that lineage actually reflects Indo-European admixture.
The original Altaic people belonged essentially to haplogroups C3, Q and N. They were joined by R1a in the Bronze and Iron Ages. In the Middle Ages, Altaic speakers left their homeland to conquer most of Central Asia, where they picked up a lot of the local Indo-European R1a lineages before reaching Kurdistan and Anatolia.
So if there is one haplogroup that links up all Uralo-Altaic people it is N.