Searching day school & boarding for girl

You haven't mentioned the city or state that you are in. Which part of the country would that be? The medium of education varies between different zones. It would be easier to provide information if you provide more details.

Juana has rightfully mentioned in her observation above that if you tell your place of living then we can do some research to find out the exact institution which can help you in this regard. In absence of that we can only give some general information about this and that is as follows.

There are a large number of residential schools in our country but these are generally expansive. You are in search of a boarding school which is not expansive. In that case you have to enquire about the Navodaya Vidyalayas which are being set up in many rural areas as per the Govt policy of providing education to poor people. Find out the nearest Navodaya Vidyalaya near your place and try to get admission there. Further, there are some schools being run by Ramakrishna Mission, Vivekananad Kendras and Missionary organisations in various parts of our country especially in Eastern sector and Rajasthan and if such a college is in your area or near to you then you can take advantage of that.

There are many schools which charge very less and give a good education. But they are available in some places only. So you should specify in which city or area you want the details of such schools.
In Hyderabad, there are many Christian missionary schools where the charges are very less and education is very good. Similarly, in Visakhapatnam, there is a school run by Sarda Vidya Peeth. A very good school. Like this, we will find a good school for poor children in almost all places.

You did not mention specifically your economic background and as such I am giving a general guide - line assuming that you hail from from a weaker status. However, you must be optimistic and you may look out some areas where the Christian- missionary are operated. In Ranchi, St Joseph School is being run for the male students and provide them food and lodging at an unbelievable price range for the poors and for the girl students they too provide shelter in a different campus with the same concession.
You will have to look out in your area whether there is any Navodaya Vidyalaya in your vicinity. These schools are government aided schools and these institutions promote the poors regardless of the sexes to sustain their studies with the enough concession offered by the government with respect to their expenses in food and education.
A thorough research would help you to resolve your issue.

A lots of thanks to all for your valuable response. And I am residing in Delhi. And want near side schools to be preferable

Without knowing the region/state where you stay and your budget, no practical advice can be given. You can try to send the girl-student in Jawahar Navodaya Vidyalaya in your district or in the Kendriya Vidyalaya with the residential facility.

Without further details, no meaningful advice can be given. However, I feel that the girl should not be sent to any school funded by any religious community.

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.

Now as you have specified your place of living we can pin point the institutions which can be approached by you for this noble purpose. One such organisation is 'Vidya' a non profit NGO which is pioneer for education to the underprivileged. Their Head Office is at Block-S, Plot No. 3126, DLF Phase III, Gurgaon, India. You can reach them by phone at - 0124 4049559. You can view the details at www.vidya-india.org

They have a very good school for the underprivileged in Gurgaon having about 1100 students at present in the campus. You have to find the modalities of admissions there. Most of these children are from slum background and their parents have income of less than Rs 10000 a month.