Praise be to Allah.
It is not stipulated that the poor person who is fed in expiation for breaking an oath (kafaarat al-yameen) must be an adult, because what is required with regard to the one who is fed is that he should match the description of being poor and needy only. If the child is poor and does not have enough to suffice him, and his guardian is also poor, then in this case it is permissible to feed him with food offered as an act of expiation.
In Fataawa al-Lajnah ad-Daa’imah li’l Buhooth al-‘Ilmiyyah wa’l-Iftaa’ (23/11-12) it says:
The expiation for breaking an oath (kafaarat al-yameen) is to feed ten poor persons, giving them food of average quality.
The poor (masaakeen, sing. miskeen) are those who can find some of what suffices them, so they should be given something to complete that.
If children are miskeen because they or their guardians are poor, then they should be given enough to suffice them. … End quote.
Permanent Committee for Academic Research and Ifta’
Shaykh ‘Abdullah ibn Qa‘ood, Shaykh ‘Abdullah ibn Ghadyaan, Shaykh ‘Abd ar-Razzaaq ‘Afeefi, Shaykh ‘Abd al-‘Azeez ibn ‘Abdillah ibn Baaz.
The amount of food to be given in expiation for breaking an oath has been explained in the verse as being of the average type of food that the person who swore the oath usually eats.
Allah, may He be exalted, says (interpretation of the meaning):
“So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families”
Ash-Shawkaani (may Allah have mercy on him) said:
What is meant by average here is that which is in the middle, not too expensive and not too cheap. It does not have to be the best quality food. In other words, feed them with the average type of food that you usually feed to your own family. You do not have to feed them with the best food, and it is not permissible for you to feed them with the worst food. The apparent meaning indicates that it is sufficient to feed ten people until they have eaten their fill. End quote.
Fath al-Qadeer (p. 391).
What you must do is try to give your kafaarah (expiation) and zakaat to poor Muslims in the country where you live.
If you do not know of poor Muslims in your country who are entitled to it, or there are others who are in greater need than them, or who have been stricken by hardship or calamity, among poor Muslims in another country, then there is nothing wrong with you sending your kafaarah or zakaah to them, or appointing trustworthy people who will deliver it to them on your behalf.
If you do that, then you have fulfilled the obligation of expiation, and it does not matter if there is a difference in the price of food in different countries, because what is required in the case of expiation is to feed them, or to give food to them. What is required is not the value of the food, whether in your country or in their country.
Please see also the answer to question no. 4347.
For more information, please see also the answers to questions no. 66293 and 145096.
And Allah knows best.