It is nice that you want to fund the boarding for a poor school girl. As you have your own limitations of budget to spend, you are searching for a govt boarding school.
While appreciating your good intention, I would suggest that you need not search alone and take the full burden on you. You try some other established sources where there is a well set system to help such deserving students.
First ascertain whether the student belongs to a community or SC/ST category, for which governments have schemes for funding education and boarding .
If otherwise, discuss with the school authorities where the girl is to study and tell them your intention to help. As they are in the field they will be able to guide you properly. Discuss with the local Panchayat ward representative or discuss with the local Panchayat Official and get help from them in this regard.
If the girl is a meritorious student, there are many organisations that come to give educational financial assistance. If the student is not your close relative, then discuss with her close relatives and only with their concurrence and support you take the initiative.
Alternatively ask her parents or other capable close relatives to search and finalise the school and hostel. Tell them the maximum you can finance. Then regularly send the money to the hostel/ school directly. Ascertain if any scholarship or grants are available for the student under some scheme.