As there are no records showing on Scotland’s People for a William Kerr/Mary Mcorquodale marriage, or a likely birth for Matthew Kerr in England or Scotland, this record may be worth considering. I could of course be totally wrong! Perhaps put it on the back burner until there is more corroborating evidence.
26 Sep 1883, Matthew Mcalone McCorkindale, illegitimate son of Mary McCorkindale, Farm Servant, was born at Parklee (Parklea) Farm by (can’t read) Parish of Kilmacolm, Renfrewshire. The informant was Mary Mccorkindale, mother. Registered 15 Oct 1883 at Kilmacolm
1883 MCCORKINDALE, MATTHEW MCALONE / M/ KILMACOLM/RENFREW 569/00 0060
Attaching the bit I can’t read!