Usually, a case under Section 406 IPC is triable by the court of a Magistrate of First Class, and not by the Court of Session, and the appeal should go to the Court of Session and not to the High Court.
Anyway, since you mentioned that the conviction order is passed by the District Court (i.e., Sessions Court), the appeal will have to be filed before the High Court. The time limit for filing the appeal in the High Court against an order of conviction in such a case would be 60 days.
You have said that the sentence is for 2 years. In such a case, it should have been possible to get bail after conviction (under Section 389 of the Criminal Procedure Code) from the trial court itself, since the trial court has powers to suspend the sentence where the sentence awarded is up to 3 years. In any case, at the time of filing of appeal in your case in the given facts, generally speaking, the chances of getting bail from the High Court during the pendency of the appeal, are reasonably good and the bail may generally be granted at the earlier stage itself. This is, of course, the general experience and ultimately it is the discretion of the appellate court.
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