You'd think you'd have a federal constitutional right to appeal, but you don't. It's not in the U.S. Constitution. McKane v. Durston, 153 U.S. 684 (1894) stands for the proposition that the states don't have to offer you the right to appeal. If they offer anybody an appeal as of right, they have to offer it equally to both indigents and those that can pay, including appointed counsel. They don't have to offer appointed counsel for petitions for discretionary review nor for writs under the federal constitution.
Assuming that there are to rights to appeal in your state's constitution, it is vital that you check the statutes that you are relying on to claim your right to appeal and the appellate court's jurisdiction to hear it.
Where you have to get relief from a trial court in a proceeding from which there is no appeal, a writ of habeas corpus is how you get it. Elsewhere in this blog I've written about some of subtleties and pitfalls of seeking a writ.