Hello !

I don't know what the difference between " ENSG00000002586.1" and "ENSG00000002586.19_PAR_Y" in  Ensembl gene/transcripts ID means.

How do you deal with these ID with "_PAR_Y"  in RNA-seq mapping process ?

Thanks,
It means the gene has multiple copies in the [pseudoautosomal regions][1]. The '.1' part is the version number.  
How you deal with them most likely depends on whether you care about these regions.


  [1]: https://www.ensembl.org/info/genome/genebuild/human_PARS.html