As a child, Damon had no contact with Allegra until the day of her 17th birthday when she found him. He felt the need to protect her from her uncle, so rejected her even though he did actually want to be with her. The lesser of two evils was to have her hate him and be safe than to have her with him and endanger her life. But that night, Damon was horrified as he watched his brother change his daughter before him. Leaving him, Damon left Mystic Falls. It wasn't for another century or so that Damon met his daughter again. After a run in with Klaus, she had came to search for Damon to prove Klaus wrong about their relationship. Which they both did as they spoke honestly about everything, before Damon surprised Allegra by asking for her forgiveness for what he did in the past and they've since built a strong relationship.