At first, Harry may be in denial. He might not be able to accept that Sirius, who has been so important to him, would do such a thing. He could keep trying to reach out to Sirius, sending owls or trying to visit him, until he finally realizes that Sirius is serious about disowning him. Then, he may go through a period of self - reflection, thinking about what he could have done wrong and trying to improve himself in case there was some truth to Sirius's actions.
Harry could also be angry. He might feel that Sirius is being unfair and not giving him a chance to explain. This anger could drive him to try and find out the real reason behind Sirius's decision on his own. He may start to investigate and dig deeper into the situation, believing that there has been some mistake. In his anger, he could also lash out at those around him who he feels are not supporting him or are taking Sirius's side too easily.
He might be extremely hurt and confused. Harry has always seen Sirius as a sort of father figure, so being disowned would be like a huge blow to his emotional stability. He could become withdrawn and start to question his own self - worth.
One possible plotline could be that Sirius Black has been under some dark magic influence. Maybe a powerful dark wizard has managed to manipulate his mind, making him believe Harry Potter is a threat to him or the wizarding world in some false way. This could lead to a series of events where Harry tries to prove his innocence and figure out what's wrong with Sirius. Another could be that there's a misunderstanding based on some prophecy or false information spread within the wizarding community. Sirius, being impulsive, jumps to conclusions and decides to disown Harry without fully understanding the situation.
On the other hand, he could feel ashamed. If he realizes that he has truly made a mistake, seeing his father so angry and disappointed could make him feel bad about himself. He might lower his head and not say anything, with a look of guilt on his face.
As time goes on, Harry could start to explore what it means to 'please' Sirius. He might recall their past relationship, the things Sirius likes and dislikes, and try to use that knowledge to his advantage. He may also feel a sense of loyalty towards Sirius that, despite the odd circumstances, makes him more accepting of the situation. For example, he might remember Sirius' love for adventure and try to engage in some magical adventures with him in a way that 'pleases' him.
Sirius would probably be overjoyed at first. Harry is his godson and he cares deeply for him.
Sirius might immediately pull Harry into a tight hug. He would be very protective and try to comfort him. He might say some soothing words like 'It's all right, Harry. I'm here for you.'
Harry may also feel a sense of adventure. Despite the situation, he's used to facing strange and dangerous things. He might start to think about how he can use this situation to his advantage, like finding out more about his parents or the secrets of the wizarding world that Sirius might know. He could be a bit excited as well as scared. For example, he might be thinking that this could be a chance to get away from the Dursleys for good.
Sirius would probably be very worried and immediately try to help Harry. He might use some basic healing spells he knows.
In some fanfictions, Sirius' character develops a greater sense of responsibility. When he rescues Harry, he realizes how important it is to be there for him, not just in times of physical danger but also for his emotional growth. So he becomes more of a mentor figure.
Sirius' character development could involve him coming to terms with his own past traumas while rescuing Harry. He may have to face his fear of Azkaban and the dark magic that he has encountered in his life. As he rescues Harry time and time again, he becomes more confident in his own abilities and his place in the fight against Voldemort. He also starts to see Harry as more than just James' son, but as an important part of the wizarding world's future, which makes him more committed to protecting Harry at all costs.
He might be initially embarrassed, especially if he receives it in a public place like the Great Hall.