No payment of salary even after working for 1.5months

Try waiting a bit more.

Dear Sir,
You have to wait for some more time to get your salary. Be aware that if you make issues then you will be in problem since your service is on probation.

Dear client kindly make complaint before HOD and if they not respond you then eventually file writ petition into high court

U should sent a written complaint to head of department of education/ higher education and even if you don't receive salary thereafter, file a writ petition before high court.

Dear Madam,
You have stated that you are working in a Government School, but not mentioned the name of the Government( either State Government or Government of India).
You are governed by Service Code ,Conduct,Rules and Regulations.
As you have stated the date of joining, you will be paid from 20th August to 31 st August. and from 1 st September to 30 th September and will continue month wise there after..
The Government and bureaucratic process takes time e.g, your Clerk will prepare the Bill, will send it to the Inspector of School, and Inspector of School to the Treasury of the District or Sub Division , then money will be coming to the School through the same route which means it will take time.For the new entrants it takes time as it goes to the State Education Directorate.
Under the circumstances it will not be wise to go the Court of Law.
Better to talk to a Retired Head Master/Principal of a Government School or a Lawyer dealing with Educational cases. They will tell you and guide you better. Any doubt at this stage?
Best of Luck.
Shanti Ranjan Behera,
Advocate through Vidhikarya.com