Short answer, "yes."
Long answer: Yes and no. In the books, Edward's protective attitude towards Bella brings unnecessary harm and turmoil. As the character often points out himself, had he left her alone, she would be far safer.
However, the problem with the characters is that you can't apply simple human terms to what is going on in the story. It's not a simple love story about two races meeting and finding an understanding. In fact, "overprotective" probably isn't a good word to describe the way that Edward acts around Bella. Edward constantly puts himself between Bella and danger, as well as Bella and other things he doesn't deem right for her. His actions are more "possessive" than "protective," and it shows if you look into the work.
Edward admitted that he could not give up on Bella, and that if he could not have her, he would rather die (as shown by his trip to Italy). The behavior is typically seen in stalkers, though he managed to avoid the stereotypical "If I can't have you, no one can!" and left Bella alive before his attempted suicide. There is also the fact that Edward tried to limit Bella's interaction with people he deemed "unfavorable" or "unsafe" for her. His actions may look like he is being overprotective, but it seems to be more of a "protecting what's mine" situation.
Of course, Bella doesn't really help his overprotective/possessive conflicts. She is either trying to stay as close to him as possible, or trying to rebel to see other people. She cant make up her mind about what she wants, and comes across as a victim of Stockholm Syndrome that is still conflicted about remaining with the abuser/keeper.
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bcoz he kept ignoring her
Jacob
The conflict between Edward and Jacob stems from their love for Bella. They are both madly in love with her but Bella feels a love like no other for Edward and only a brotherly love for Jacob. Bella believes the two do not get along because they are so much alike.
she ends up with Edward and they have a baby.. but she gets very close to Jacob in new moon when Edward leaves her. but in the end she chooses Edward.
In Breaking Dawn Edward tells Jacob the he can kill him if Bella dies seeing as he doesn't want to live without Bella. At first Jacob agrees however later on, once they believe Bella to be dead, Jacob says he will not kill Edward as he wants him to suffer.