Sessegnon was linked with a move away from the Stadium of Light last summer after he failed to settle in the North East.
But he insists his problems are now resolved and added: "I didn't think about leaving and I didn't think about what was being read about me.
"The issue with my family is settled. Two years ago when I arrived, sometimes my family wasn't here but now it is fine.
"They live here now. This problem is completely finished. I know the fans love me and I love the fans right back.
"I am not a player who likes to talk. I prefer to play. My football does the talking for me."