Is it better for a Muslim to perform the Udhiyah (sacrifice) in the country where he studies, where there are no poor Muslims, or to delegate someone in his home country to perform the Udhiyah?

The default is for a Muslim to slaughter their sacrificial animal in their own location and to perform the slaughter themselves. This is the prescribed method, following the example of the Prophet (peace be upon him), and the purpose of the sacrifice is to manifest a religious ritual, not merely to obtain meat.

However, if the sacrificer is in one country and their family is in another, it is preferable for them to offer two sacrifices: one in their own country and another where their family resides. If they are unable to do so, there is no harm in sending money to their family for them to offer the sacrifice on their behalf in their country. This is because it brings joy to their family and addresses their urgent needs in some countries.