On one hand, the answer is no, Eve did not eat an apple. Genesis chapter three records this account of Adam and Eve’s rebellion against God. In particular, Gen 3:6 says that Eve ate a fruit. Since the variety of the fruit is not recorded, it is impossible to say whether it was an apple - it could just as well be a pear or banana.
On the other hand, the answer is yes, the eating of the fruit did lead them to being thrown out of the garden. As you read the passage further, we find that Eve gave some of the fruit to her husband and they both eat. As a result, they were both ashamed and hid from God. God punishes them with a series of curses (Gen 3:14ff) culminating in their banishment from the garden (3:22 - although it is possible that this banishment is a blessing). This cause of this exile is not only Eve but Adam is indicted as well (eg. Adam is held ultimately responsible for the sin in Romans 5). While Eve is in error by listerning to to the serpent, doubting God’s goodness and starting the chain reaction; Adam is equally guilty in failling to stop the rebellion and in not making a stand for God’s word - after all, he was given direct instructions by God (Gen 2:16-17). But he chickens out(!) and abdicates his responsibility to take care of his wife and creation. Ultimately, they are both guilty for, in their own way, they both doubted God’s goodness and made their own rules to follow instead. And you know what, we still do that today.
Therefore, the answer is ‘no, she did not eat an apple’ and ‘yes, she ate a fruit that lead eventually to them being thrown out of the garden’.