What are achild’s rights of inheritance?

First, you need to find out whether or not your father had a Will. You can ask family members or his friends if they know if one was drawn up.  If so, then if you were a beneficiary you would have been notified.  If your father did have a Will and it has been filed, you can go to the Probate Court in the county where he resided at the time of his death.  Once filed it would be a matter of public record and accordingly it can be viewed by anyone (for a small fee.      

You should be aware however that some assets can be transferred outside of probate.  For example, if your father had a small estate, property may have been transferred by affidavit or otherwise.  Additionally, some assets may have been held as "joint tenants with right of survivorship", in which case the other joint tenant would have received your father's share to property operation of law.  In addition, funds in an IRA, pension, 401(k), or other retirement plan bypass probate and go directly to named beneficiaries (unless the beneficiary named was his estate).  The same holds true for any life insurance proceeds (and as to such proceeds, unless you were a named beneficiary.

Additionally, even if he had a Will, a parent may disinherit their child.  Children typically have no right to inherit anything from their parents.  Although, as a general rule in such cases, there should be specific disinheritance language in the Will; most states do have laws to protect against an accidental disinheritance.  For example, if it appears the parent did not know about a child; or if the child was born after the Will was signed.  In such cases a child may have a right to “elect against the Will”; that is they have a right to certain assets.  Otherwise, if there is a Will and you're not in it, you are unfortunately not entitled to anything.