Refused To Let My ExWife's Affair Child Call Me Dad & Now They Blame Me Cos He's Being Teased~ AITA

I (38 M) had a fight with my Ex-wife(41F) about her child Sam (7m), and need an opinion from outside.
We have a son together, Jake (9m), but Sam is not mine. Our divorce was caused by my wife's infidelity, and I told upfront to ex when she was pregnant that I will never take any responsibility for Sam, not emotionally nor financially.
However, I have figured my emotion out and got them in order to protect my Son Jake. That includes accepting Sam as his little half-brother, and allowing him on special events to visit me and Jake. Our custody agreement is clear, every second weekend Jake visits his mom.
So, my son had his birthday last month, where I allowed Sam and Ex to visit and celebrate with us. It wasn't something big because of the global situation, just about 15 people (Jake’s friends and some family members).
Sam loves to mimic Jake, and when he saw him calling me Dad, he started to call me dad too. I spoke with him calmly and told him that I don't want to be called dad by him, but he is allowed to call me by my name. When he had asked why, I explained that he is not my child and I am not his dad. Then he asked me who is father is, and I respond that I don't know.
Story 1:
AITA. I had a fight with my Ex over her Affair Child, our son picked it up and is now rejecting his Half-brother.
Story 2:
AITA for taking my son on a trip I knew his stepsiblings wanted to go on?
Story 3:
AITA. for using some of my stepson's camp savings to buy a replacement sneakers for my son?
Story 4:
AITA for not leaving with my newborn twins and toddler while my sister had a meeting
#AITA #Parenting #Family