I have a cousin whose father just passed away without a will. He is survived by his spouse, his wife, but deceased spouse declared to the whole .family that he does not want the child to remain with the mother but his brother. THe problem is that it was not written down as a will. Now the surviving spouse is ignoring the verbal will and refusing to cooperate. The father’s family had much more involvement in raising and the wife’s family recently appeared to claim responsibility to the son and take him back to the wife’s side and possibly sever any contacts with the father’s side of the family. The son doesn’t even want to be with the mother and we all know that but the mother believes she is the top figure in the situation and refuses to cooperate with anyone. The father’s side of the family had to plan out the funeral and pay mostly for it while the mother’s side had little involvement. Isn’t there anything we can do to make the deceased spouse’s verbal will final and leave the son under his brother’s responsibility, not the mother’s?

The child will go to the child’s mother unless she is shown to be unfit.
If the woman is the kid’s biological mother, you have zero chance. If she’s the stepmother, feel free to waste your money in probate court, but you’ll probably still lose barring any facts that she’s crazy and had been married to the father for some ridiculously short period of time.
No, you cannot do that. Children are normally under the custody of their parents. If one parent dies then the other parent automatically gets custody. Even if the deceased parent had clearly stated in the will that the custody should go to someone else, it would be invalid. Only if both parents die can the custody transfer to someone else based on the will.
The only way I can think of for the brother to take custody would be if the son is in an unsafe situation with his mother. In that case, you could have the child put into foster care and then adopted by the brother. But that is a long and difficult process, and requires solid proof of abuse.
Without a will, the child would go to the surviving biological parent.
Unless by some miracle, your cousin decided to amend his will and changed guardianship of his son over to his brother and the will wasn’t found yet, you really don’t have a case.
A will is the ONLY legal document in which a person can state their desires regarding guardianship of their minor children. Verbal statements to ANYONE are worth the paper they are printed on. Even with a will, a surviving spouse is most likely the legal guardian under the law wherever you are. If you wish to dispute the mother’s claim, you NEED a family law attorney.
Note: There is NO SUCH THING as a verbal will, unless it is one tape. Even then, it is not legal in all jurisdictions.
Child goes to mommy. If you want protest it then you need to get a Probate Lawyer and head to Probate Court.