You have consented by your free will. The company can claim that you can not rescind the contract signed by your own free will.
If you are sick you can always apply for sick leave and take benefit of mediclaim/group insurance/ESIC etc provided for by the company. The employer has not terminated you due to sickness. The employer has not asked you to resign due to sickness.
It is mentioned that the employment ‘at will’ by the employer.
This is inserted to indicate that the employer is reserving the right to end the services as and when it pleases.
Indian Law does not concur with ‘At Will’ in case of personnel that are covered by the def. of ‘Employee’, ‘Workman’.
There is also a clause on Arbitration at Hyderabad.
The ground for service agreement is stated as Training!
Has any training been provided that added to your qualification?
The company seems to be in AP.
The Andhra Pradesh Shops and Commercial establishments Act is o employee friendly and there are many employees’ unions/trade unions that have done good job for employees.
You should consult an able Labor law Consultant/Service Matters Lawyer/Law Firm; show all documents on record and given inputs in person. The lawyer that has examined all docs and inputs can advise you the best.