What should a person do who borrowed money from public funds that were in his custody, then things became confused for him and he no longer knows how much he borrowed and how much he repaid, and whether his private money mixed with public money?

You are not permitted to borrow from the funds deposited with you except with the permission of their owners, because disposing of them without permission contradicts trustworthiness (amanah). You must seek forgiveness and return what you took to its owners if possible. Otherwise, give it as charity on their behalf. If you meet them and they approve of what you did, then you are absolved. Otherwise, pay them their due, and you will have the reward of charity.