It appears you went offline without seeing my request for some additional information. Because I don't want you to have to wait any longer, I'm going to go head and answer as best I can without knowing those things.
Birds don't bite because they hate someone. They bite because they are either scared or feel somehow threatened (their food, a toy, etc. is being protected. Regardless of how long you have had your bird, the best thing to do is start over. Pretend you just got him. For the first week, it would be a good idea to keep the cage partially covered to make him feel more secure. Don't try to touch or handle him in any way - just provide basic care in a calm, quiet way. Put the cage in a room where you spend a lot of time. That will help him get used to your presence and to help him realize that when you move about, he's not in danger. Talk softly to him from outside the cage, but don't try to put your hand in until he feels comfortable in your home. For many birds, that will be after about two weeks of becoming accustomed to family activities and listening to you talk from outside the cage.
At that point, you can offer him a treat, or just let your hand rest quietly in the cage. When he's at ease with that, gently rub your finger on his breast, just above the legs. That may encourage him to get on your finger.
When he's on your finger, stay close to a perch so he can hop off. He's learning that your finger is a safe place to perch. The following site has very detailed step-by-step instructions on finger taming. I recommend it for tips on the next steps. It applies to cockatiels, as well as parakeets.
Don't try to hold him. Many birds don't like being held, and will take months to get used to that. There are no shortcuts to taming - you'll need patience and will simply have to spend time at each stage before moving on. If at any time, he is uncomfortable with the stage you are at, back up to the last stage where he was fine.
If you have more questions, let me know in a REPLY. With enough time and patience, almost any bird can be tamed. It certainly takes longer with one who has had little interaction when young. I wish you success.
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