An expert told the trial Sean's injuries were consistent with the tot being shaken, reports Bristol Live.
Clark told the jury at Bristol Crown Court fatherhood didn't daunt him.
He said: "I liked it, I enjoyed it.
"I found some stuff quite difficult but I got through it."
But Sean was found dead on Sunday January 14, 2018, when he and his parents spent the weekend at Clark's mum's home in Warmley, Gloucestershire.
Paramedics who arrived on the scene promptly found no signs of life and no external injuries.
A spokesperson for the NSPCC in the South West said: “This is a deeply upsetting and disturbing case in which a baby was killed by his own father.
“Babies and young children are entirely dependent on those who care for them and we all have a duty to look out for their welfare.
“Anyone concerned about a child can contact the NSPCC Helpline on 0808 800 5000, while young people can call Childline on 0800 1111.”
Clark will be sentenced on September 24.