how to prove marriage

For gender laws formal marriage is not essential. Marriage like relationships are sufficient. As you have a son that is sufficient to prove marriage like relationship.

If both of you are adults you can go before a registrar of marriages and get a registered marriage. If both of you are Hindus you can get a Hindu Marriage certificate. If you belong to two different religions you can marry under the Special Marriages Act. Go to the nearest office of registrar of marriages in Keralam and seek advice. It would be better if you take a lawyer with you.

@avniz aggarwal

You can file 454 bigamy case also against him. His child with you is a strong point. You can certainly ask for compensation for the care of the child.

Proving a marriage is difficult. That is how most film stars merrily marry again and even publicly say that they have married (for the second time). They also get elected as MP's or MLa's.  They get gun salutes when they die. They escape because their (second) marriages are not legally valid. Also bigamy is not a cognisable offence. You have to prove two marriages i. e. your marriage and your husband's marriage to the other woman. As both of you have children you can make an attempt. File a case and find out which marriage your husband denies. In any case you will be able get maintenance at least in the name of your son  First ask for maintenance for both of you.