The husband of my sister left a year ago, and abandoned his child because they had marriage problems. My brother in law, at first gave a financial support but time goes on he failed to give because the company where he belong deduct almost half his salary, sometimes he give promise to his child to give their allowance on that day but when the day comes he failed again for another reason. He had a deal with my sister that monthly he provide financial support but as we observed he just always make promises.

May we ask if my sister have authorized to file case against her husband, and we also heard from the sister in law of my sister that her husband had an affair to other woman.

Your general location would help greatly, as local laws vary, but I certainly think that this woman can file for child support through the courts. Many men make promises they can't keep to keep women out of court, and not file for divorce, or child support.

A court order is better than a promise thats NOT kept.

Your sister NEEDS to take him to court for child support and maybe spousal support. I don't know what you mean by authorized to file case.

He is merely not paying support, you never mentioned if there was a court order ?

It does not sound like it. She takes him to court, get court ordered child support, what is proper percentage for his pay, ( there is normally a chart for your location)
But seldom is it half of his pay. More normally it will be about 25 percent of his pay.
But that is just a average.

Then she gets a garnishment from his paycheck.