DoI have any rights to my estranged father’s estate ifI am his only child?

First of all, did he have a Will?  If he did not then he died "intestate". This means that the intestacy laws of the state where he was domiciled at his death will control.  Typically, in such a case, a surviving spouse will get 1/2 - 1/3 and the remaining children split1/2 to 2/3 (in your case this would be entirely yours since you are an only child).

If your father had a Will, then you may or may not be entitled to anything. 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.

Notre:  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.