Once the inheritance is deposited into your account, a creditor could conceivably attach it if he gets a judgment and avails himself of the garnishment process. However, to my knowledge the child support agency doesn't attach bank accounts as long as payments are being made, with the exception that they do grab IRS or state tax refunds.
John is right but when money is in your account, the general rule is that anyone who is owed money by you and who has a judgment also has the right to garnish the account to get paid on the judgment. You may have the right to contest the garnishment's legality after the fact for certain reasons stated by law only. Note: if this answer was helpful, check the box below.