I need to setup periodic faces on Y-type block (on adjacent faces of H-type block). I have to choose two vertices, but I have only one (e.g. on axis)! It`s a typical situation for axisymmetric problems.

What can I do in this situation ?

You need to pick the same node twice - essentially making it periodic with itself so the face is periodic. There seemed to be a glitch in 10.0 - so watch how it puts the vertex numbers in the entry area as you may need to type the same vertex number there twice if the mouse selection doesn't let you select the same vertex twice.