Murphy's from Cork

Hello all!! First message for myself and am excited!! My great grandfather, Jeremiah Murphy supposedly from Cork was born circa 1863 to 1870. His father was supposedly also a Jeremiah. It is unknown what his mothers name was. Quite sure they were catholic. He emigrated to Cleveland, Ohio circa 1887, can not find ship manifest details. My mother said he was a troublesome sort and supposedly in the IRA and fled Ireland for his safety. He has. Even my brickwall for years. My ancestry DNA came back as 65% Irish with counties of Cork, Tyrone, Londonderry and Antrim. Thank you all, looking for any relatives of Jeremiah or any info on his parents. Thanks again!!