To simplify things, I'll put it as if it were my father:
My mother conceived me without being married, and my father never acknowledged me. I don't remember ever having met my father.
What is this kind of "biological-only" father called?
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I'm not sure why no one has said it, but the best answer is right in your question:
I may have inherited a heart condition from my biological father.
I have a situation similar to the one you describe, and my whole life this phrase has never failed to convey the meaning of the genetic-only relationship.
If you're looking to emphasize his lack of involvement, a common description for a father-by-biology-only is: "sperm-donor". (US)
Note that this term is often used outside the context of a formal sperm donation arrangement, usually pejoratively, emphasising that biological father did not provide a parenting role.
Try birth father also called a biological parent. It means a biological mother (birth mother) or biological father(birth father).
Here is a definition from another site. This site defines it as the man who was someone’s father when they were born rather than the man who has adopted them. It is closer in meaning to what the op asked.
I'd say that all that he is, is progenitor.
A person or thing from which a person, animal, or plant is descended or originates; an ancestor or parent:
'his children were the progenitors of many of Scotland’s noble families'
In my mind that properly defines both the role in siring and the lack of any involvement afterwards.
Unfortunately, the term Baby Daddy seems to be the term most used in common practice today. This seems to have started with descriptions of celebrities and their children in the tabloids. This term has deplorably now entered the common nomenclature.
Baby Daddy - slang: the biological father of a woman's child; especially : one who is not married to or in a long-term, intimate relationship with the child's mother http://www.merriam-webster.com/dictionary/baby%20daddy
I guess you could describe them as your estranged biological father
to cause someone to be no longer friendly or close to another person or group
If you're able to change the usage a bit, I'd offer sire. Changing the usage to something more like:
Having been more sired than fathered, I never knew the man.
helps to differentiate between that alternate meaning of sire, which is a title of respect and nobility.
There are several terms, the best one to use depends on nuance. To express the connotation of a parent who should have been there but wasn't, use the (mildly) pejorative term absentee father.
absentee: a person who is expected or required to be present at a place or event but is not. Google
So many names for this chap. Here's another one: genitor.
The word comes up every now and then in Countdown, a letters and numbers quiz in UK, that's how I know it.
Many words have been used, but I don't think anyone mentioned that different terms are appropriate for different situations.
"Biological father", or more unusual "genetic father" just describes the biological situation without any judgement. It will even be used to describe the husband of the wife who raised the child in cases where people doubt it. "My husband is indeed the child's biological father".
"Sperm donor" in situations where a male was just used to produce a child, without intention on either side for that person to enter the role as a father.
An "absentee father" is a person who is supposed to be there as a father but isn't. An absentee father may be absent since before birth or left yesterday. "Estranged father" is a person who isn't there anymore. The "estranged" means he wasn't always absent.
"Deadbeat dad" is an insult for someone who doesn't meet his legal obligations.
"Baby daddy" is just ridiculous.
Seems nobody did think of situations where the biological father doesn't know he's the father, where the biological mother doesn't know he's the father, where the child is adopted and never meets any of their biological parents, or where the mother just finds a better father for her child.
This may not be what you're looking for, but I thought it would at least be related to the question and interesting for a non-English speaker.
There are people that make a strong distinction between "Dad" and "Father".
A father is someone who believes that by donating his sperm for your creation, he has done his duty in life. A dad is someone who gets up every day and does whatever he can to put a roof over your head, clothes on your back and food on your table.
In my personal experience, this distinction tends to be made by people who have either a bad father or a bad step-father. Also, some people have the opposite associations of the words (father is loving, caring, dad was just the sperm-donor...). For instance, there is a song lyric from the popular 90's band Nirvana in which the singer wishes his father would have been more involved:
I tried hard to have a father. But instead I had a dad.
In this case, dad has a bad connotation.
The dictionary definitions of the two words don't match these perceived meanings, but when speaking with certain people, you might get corrected on your word choice.
Your father is your father, the father you never knew. There is no special word for this all-too-common situation. Don't judge him too harshly until you hear his side of the story.
Birth father can't be right, since fathers don't give birth. Birth mother is redundant: mothers give birth, even if maybe some other generous, or merely put-upon, lady brings you up.
Words are tools, and using a tool the wrong way damages it. A new hammer you can always buy, a new language - not so easily.