no
When the US Supreme Court issues a writ of certiorari (an order to the lower court to send up records), it indicates they have agreed to review the case under their appellate jurisdiction.
Lawyers do not send summons, that is a document that is issued by the court with jurisdiction in the matter. In some cases and in some US states a summons to appear in a civil case can be sent by certified mail.
In the US visit the family court where you live and check the index of names to see if there is a case file under your father's name. If you suspect he has a child in another jurisdiction then you must check the family court records in that jurisdiction.
Magistrates typically have two types of major functions: to preside in court hearings for bail bonds, or to preside in minor civil and criminal actions, generally small claims court or in criminal proceedings with minimal maximum penalties. In bond court a magistrate has the right to decide if there is enough probable cause to send the case to its proper court of jurisdiction, and to assign any reasonable bail according to the law.
Remand
send the case back to the lower court
Your next step would be to appeal your case to the Court of Appeals for the particular Disctrict Court in which you were convicted. They will review it and either agree to review it, affirm it (they agree with the trial court), or remand it (send it back to the trial couort) for further action.
A "Writ of Habeus Corpus" is presented to the court having jurisdiction in the circuit where the detainee is incarcerated.
The Supreme Court of the United States has full discretion over the cases reviewed under its appellate jurisdiction. Appellants submit a "petition for a writ of certiorari," asking the Court to consider a case. If the Supreme Court believes the petition has merit, they may grant certiorari (grant cert) and issue a writ of certiorari (order to the lower court to send case records). When the justices grant cert, they are essentially granting permission to the petitioner to bring a case before the Court.
When the US Supreme Court agrees to hear a case, it issues a legal order called a "writ of certiorari" telling the lower court to send up the case files.
The "document" is a court order called a "writ of certiorari."
send the case back to the lower court