Praise be to Allah.
The scholars are agreed that the menstruating woman should not fast, and that her fast is not valid if she does fast, and that she has to make up the days that she did not fast in Ramadaan because of her period.
See question no. 33594.
What you have to do is to make up those days, and repent to Allaah for your failing to seek knowledge, which led you to commit this haraam action.
If you will be able to make up these days in the same year before the next Ramadaan comes, then all you have to do is to make up the fasts, and you do not have to feed the poor.
But if you delayed making up the fasts until the next Ramadaan came, with no excuse, then there is a difference of scholarly opinion in this case: should you feed the poor as well as making up the missed fasts, or not?
We have already stated in the answer to question no. 26865 that you do not have to feed the poor.
But if you want to be on the safe side, and you feed the poor as well as make up the missed fasts, that is good.
What is meant by feeding the poor is feeding one poor person for each day, giving half a saa’ of the local staple food, such as rice or dates. Shaykh Ibn Baaz stated that this is approximately equivalent to one and a half kilograms of rice. Fataawa Ramadaan, p. 545.
The majority of scholars are of the view that it is not sufficient to pay the monetary value of the fidyah (ransom), so you cannot pay money; rather you should give the actual food to a poor person, as stated above.
The Standing Committee was asked about an old man who was not able to fast. They replied:
You are allowed not to fast so long as you are unable to do so, and you have to feed one poor person for each day that you do not fast. You can give it all at once or break it up into smaller amounts, because Allaah says (interpretation of the meaning):
“and [Allaah] has not laid upon you in religion any hardship”
It is not enough to give money instead of giving food.
Fataawa al-Lajnah al-Daa’imah, 10/163.
You can give money to any charitable organization, or to the imam of a mosque who is known for his religious commitment and righteousness, to buy food on your behalf and distribute it to the poor, and how many there are nowadays.
You could also make food for the poor, of an amount commensurate with the number of days you owe. Al-Bukhaari said: With regard to the old man, if he is unable to fast: for one or two years Anas, after he grew old, fed bread and meat to a poor person every day and did not fast.
It is permissible to give this kafaarah to orphans if they are poor, but not every orphan is poor or needy.
And Allaah knows best.