The following persons who are financially unable to obtain counsel are entitled to be represented by a public defender:
(1) a person charged with a felony, gross misdemeanor, or misdemeanor including a person charged under sections 629.01 to 629.29;
(2) a person appealing from a conviction of a felony, gross misdemeanor, or misdemeanor, or a person convicted of a felony, gross misdemeanor, or misdemeanor, who is pursuing a postconviction proceeding and who has not already had a direct appeal of the conviction;
(3) a person who is entitled to be represented by counsel under section 609.14, subdivision 2; or
(4) a minor ten years of age or older who is entitled to be represented by counsel under section 260B.163, subdivision 4, or 260C.163, subdivision 3.