A couple of questions Andy:
If you are concerned that a first cousin is not a DNA match and have questions about your father, have you considered asking him if he would take a DNA test?
It sounds like your mother may be deceased? If so, does she have any close family who may know if she had an earlier pregnancy?
My father is taking a DNA test too. If that comes back showing that we are not related, then we will - of course - take an independent paternity test to confirm the results. My 2nd cousin is convinced that my results have either been mixed up or contaminated, but I am not convinced as it seems too convenient that I've matched with lots of people on my mother's side but not my father's. That being said, I did match with one ancestor on my father's side several generations ago and I can't find any evidence to suggest I could also be connected to that ancestor via someone else on my mother's side.
I think something suspicious is going on - I'm just not sure how. I downloaded my GEDCOM file and DNA profile and uploaded to MyHeritage too to see if any different results came back. Indeed, it matched me to a woman who it identified as either my grand-niece OR a cousin once removed. As neither of my sister's have children, I have ruled the niece out as being that relationship - unless, of course, I did have an older sibling I never knew about.
What is interesting me further is that the DNA tests have identified lots of relatives in Ireland. I have contacted some of those individuals to see if they know how we might be related, but none of us can find a connection. In fact, none of us can find any evidence to suggest our families have ever met, let alone married/interbred!! It's all a total mystery.
Consequently, I am doing an additional independent test with MyHeritage to see if that spits out completely different results!!
Yes, my mother died when I was a child. The only people I knew on that side of the family were my aunts, uncles and grandparents. And it wasn't even until all this kicked off that I was able to identify great-grandparents or great-aunts and uncles. I had no idea my maternal grandparents even had siblings!
My father has agreed to ask the eldest of her siblings if she was aware of my mother having a child before me (or a pregnancy).
I feel like it's a Netflix special waiting to unfold, as there seem to be two things that would be independent of each other: 1. The possibility of having an older half-sibling; 2. The possibility that my father and I might not be biologically related either.