Ok every welcome to game theory 2 we all played Pokemon by now we start off as a trainer without a dad. Why is that well here is my game theory for it after, reading the first generation poke'mon manga American edition.
First, like every family you're around 10 you're parents got into a argument and, broke up. Usually resulting in a move with you're mother to somewhere new. Which happened in Poke'mon Ruby/ Sapphire/ Emerald versions.
In the manga of Poke'mon adventures near volume 11 when in America Ash goes to battle Sabbrina for the phyic gym badge he encounters a guy who looks like him but, older. The time line is uncertain when Ash's parents divorced. So could this man and, gym leader be his lost relatives. Most likely.
Second, the evidence seems far fetch as anyone could assume that. But, the main having black hair, brown eyes, the same z mark on his cheeks, and cloths. This makes it have to possibilities. Since Ash never has a photo of his Dad at home and, his Dad hasn't seen his soon in a long time. So neither would remember the other if time has passed so many years.
Third, if this man isn't his dad their is only one other possible one. The Gym leader Giovanni. Based on his history he could have done something to get Ash's mom upset causing a break up. Later threw his anger he created Team Rocket. As a subsitute for his family he long's for.
Fourth, if none of those are correct and, based on the poke'mon show/ ds series black and, white. Because, Ash has alot of things an yet moved again his Mom probbly enherritted the money threw the Dad's death. Since she never had a job means the father had to be reach. Meaning the best character is Giovanni. Who had a organization and, paid team rocket members.
So Giovanni is most likely Adh Catchem's fathet but, this only a game theory based on actual game/ show events and, plotline info.