Nurarihyon no Mago Kaze no Stigma Katekyo Hitman Reborn! Inuyasha Claymore Shaman King Sousei No Onmyouji Tokyo Ravens
-Inu X Boku SS -Noragami -Owari no Seraph -Kyoukai no Kanata -Hitsugi no Chaika (it doesn't have that much focus on it thought) -Yakusoku no Neverland (don't know if this one really counts for what you're looking for) -Kimetsu no Yaiba They are somewhat related with family/clan thing but isn't the focus so, keep that in mind.
Try K Project. Excuse me, what!? I don't think that's necessarily what "bloodline" means. Unless you're talking about the way to preserve it, but OP probably is not asking for that.
kenga asura (the assassin clans) basilisk mahouka you may also be interested in this list: https://tvtropes.org/pmwiki/pmwiki.php/Main/SuperpowerfulGenetics good list, but this doesn't really fit since claymores/yoma are considered entire races. I also recommend the manga more than the anime since the anime ending is generally considered to be very bad.
Animes that got family w/ unique powers/bloodline, some are not necessarily biological family: One Piece JJBA Uchouten Kazoku Nurarihyon no Mago Kaze no Stigma Joukamachi no Dandelion Kekkaishi Arcana Fagmilia Fruit Basket Fairy Tails Hunter x Hunter Kamisama Kazoku Abenobashi Mahou Shoutengai Tenchi Muyou Shounen Onmyouji Blue Exorcist Inu Yasha Ushio to Tora Sousei no Onmyouji Ranma 1/2 Garo series Tokyo ESP Soul Eater
- Arcana Famiglia - Aishiteru ze Baby - Arslan Senki - Ashita no Nadja - Akage no Anne - Candy Candy - Citrus - Clannad - D.N.Angel - Daa! Daa! Daa! - Gilgamesh - Hello! Sandybell - Mo Dao Zu Shi - Kaze no Shoujo Emily - Pollyanna Monogatari - Alps Monogatari: Watashi no Annette - Alps no Shoujo Heidi - Konnichiwa Anne - Night Head Genesis - Ranma 1/2 - The Hakkenden