My ex wife , after 9 years claims her son is mine, after I establish paternity will I be expected to pay for back child support?

Any question on law needs to include a general locale as laws vary by area.

Most areas restrict support back to the date of filing. However, some do allow retroactive support.

Was the child born after the divorce?

If you were still married, when the child was born, you will have to challenge paternity since it will be assumed you are the father by law in most areas.

But some areas do allow for awarding back. But it is not common in most areas

I married her AFTER the child had been born. We were married 2 years then she divorced and stating in the divorce papers there were NO children .I just want to be in his life and she hasn't t0ld him that I am the father. He is growing up thinking ,another man, is father . (which she is now divorcing also.)

I married her AFTER the child was born. We were married 2 years and she filed for divorce. In the divorce she stated there were NO children. I want to be in his life and she has not informed the child that I am his father. She has been remarried and had 3 more children and the son thinks her husband is his father. Now she is divorcing this man . I just want to be involved with my son now that I have learned he is mine! Any suggestions?

First you were asked for a locale. Depending on how close to the birth you got married you may be the legal father. This depends on local laws.

But the bottom line is you need to go to court to establish custody and visitation.

The location is Arizona

Firstly- does the child have a legal father?

No there is no legal fathern

The court may order either or both parents to pay child support. The court may also order retroactive child support (if no child support was previously ordered) from the date of separation, but not more than three years before the date of the filing for dissolution of marriage, legal separation, maintenance or child support. The amount of child support order shall the based on the following factors:

The financial needs of the child.

The financial resources and needs of the custodial parent.

The standard of living the child during the marriage.

The physical and emotional condition of the child.

The child's educational needs.

The financial resources of the non-custodial parent.

The duration of parenting time and related expenses.

Excessive expenditure, destruction, concealment, or fraudulent disposition of community property.