The Roman in York you are looking for is known a 3DRIF-26 and is J2-L228.

The publication can be found if you search 'Genomic Signals of Migration and Continuity in Britain before the Anglo Saxons' published 9 Jan 2016 and is available on the Nature Communications website (sorry my lowly status prohibits me from embedding a URL).

Unfortunately, the paper considered this guy an an outlier in the data as the study was looking at known British DNA and not studied further.

As someone who is J2-L26 and was born about 1 mile from the Roman city of Viroconium Cornoviorum (Wroxeter in Shropshire, England) I can't help wondering if more undiscovered J2 DNA was left behind in Britain after the Roman withdrawal.