Is it possible to ask for only tuition fee

You can certainly get maintenance for your child especially if you are not asking for any maintenance for yourself. There is no separate section for school fees. I think you can get school fees for your child unconditionally while maintenance for you will depend on many factors as pointed above. Go to Court, get some pre-printed application form for filing a petition, fill it and provide all the details.  Check the applicable Act. I am not sure you can ask for maintenance for your child under 125 Cr.P.C.  That may be only applicable if you are seeking maintenance for yourself but I am not sure. But certainly, based upon your religion and the applicable Act, there wil be sections for maintenance to be provided for your child.  You can do all this yourself. No need for a lawyer if all u want is fees for your child. I suggest you ask maintenance for your child and yourself too and let the Court decide.  Do not ask only for fees. The Court will think that you are well off and therefore not seeking maintenance for yourself. In the future it will work against you.

if you are filing for support for tution fee of your child, you file two applications. One for maintenance and one for expedited hearing citing the reasons for urgency. Only then will it be processed fast. Otherwise, it will take months.

Here is what you do:

Write a petition with the proper heading, etc. Check online and you will see some sample petitions. Specify the section under which you are filing (state ALL applicable Acts and sections for seeking maintenance so that your petition has more force). 

Then state the facts, preferably in chronological order only to the extent relevant. Do not fill pages with irrelevant allegations. Remember you are only asking for maintenance not seeking divorce. Be truthful. 

In a separate section state the reason for the urgency... provide details of tution requirements and other needs of the son and you.

Finally, comes the prayers paragraphs in which you list precisely what it is that you want the Court to order. Example, maintenance of so-and-so per month. THAT COMPLETES THE MAIN PETITION.

 Now comes the application. Again use the same cover page but instead of the word PETITION use APPLICATION.  Call it APPLICATION TO EXPEDITE THE MAINTENANCE PETITION/APPLICATION.   In this, you specify the reason why you want it expedited.

Thats it!  Show it to some advocate there to see if you have erred. Pay him/her 1000/- to just see if it is procedurally correct. Make the suggested corrections. Then go to the registrar and see him/her and show the petition and application you are about to file. Inform him/her that because of financial reasons you are representing yourself. They will suggest some changes.  Make them.  Then finally ask about how to serve the papers to the other party.  Then on the scheduled date.. be present!  YOU WILL GET A WONDERFUL FEELING OF ACCOMPLISHMENT... YOU HAVE DONE ALL THIS YOURSELF AND SAVED YOURSELF A TONNE OF MONEY AND AGGRAVATION.

You can also blank your name and other personal details and PM your docs to some advocate without disclosing your contact info. There are some very helpful advocates on this site. They may suggest some changes too...  I say without disclosing contact info because it is generally not a good practice to disclose personal info to people you meet on public sites.