What should I do regarding the days I broke my fast in Ramadan as a child, knowing that my mother prevents me from making up these days?

If you were an adult at the time of committing the sin, you must make up the days you missed fasting, and if you are unsure of the exact number, you should act with caution (i.e., make up the higher number). Expiation (kaffara) is only obligatory for breaking the fast through intercourse, according to the majority of scholars. However, if the fast was broken by something other than intercourse, then no expiation is due from you. If you delayed making up the fasts until the next Ramadan (definition) began, you must feed one poor person for each day, unless you were unaware of the obligation to make them up. The two months you fasted are considered supererogatory (nafila) and do not count as making up (qada) the missed fasts, as making up requires the intention to be made the night before. There is no obedience to a creature in disobeying the Creator; therefore, do not obey your mother if she commands you to abandon an obligatory fast.