There are no 'Gypsy genes' although there is a huge amount of bullshit around this. There seems to have been a large migration from Central South Asia around 500 AD towards the Balkans, from where the population fanned out across Europe by about 1400.
In the time since 500, Europe has suffered several population bottlenecks due to climate events and disease, multiple armies have successively conquered the nations, and there have been mass population movements. As a result, all our DNA is jumbled up; European DNA is all quite similar. Some distinctions can be observed in, for example, Sardinians and Kurds. But you couldn't look at a DNA profile and say "that's Gypsy/Roma".
This long discussion explains how researcher bias, ignorance, and difficulty of identifying sample populations has led to crashing errors in describing the genetic heritage of gypsy people. It makes interesting points (if you like that sort of thing) about the effects of ghettoisation and extermination on an ethnic group, and how those effects can be misinterpreted by academics.
Gypsies do prefer to practise endogamy but it has never been strict - there are no "Gypsy diseases" as there are for, say, Ashkenazi Jews - so the DNA is, in fact, a mixture like the rest of us.