Under Section 401 read with Section 378 of the CrPC (now Bharatiya Nagarik Suraksha Sanhita - BNSS), when a common judgment involves an acquittal for a Indian Penal Code (IPC/BNS) offence alongside a conviction, splitting the appeals into two different forums (Sessions Court and High Court) is legally impermissible. This prevents a "conflict of decisions" where two different appellate courts could pass contradictory orders on the same set of facts and evidence. Under Section 378(4) of the CrPC, if a case is instituted upon a private complaint and results in an acquittal, the complainant can only challenge that acquittal before the High Court.
You cannot file this directly. Your advocate must file an application for Special Leave to Appeal within 60 days from the date of the acquittal order. The High Court will first look into whether there is a prima facie case to admit the appeal; once leave is granted, the regular appeal against acquittal is heard.
You will file an Appeal against Acquittal (for Section 420 IPC) along with a prayer for the enhancement of the sentence and penalty (for Section 138 NI Act) in a single petition. You will first need to file an application for Special Leave to Appeal under Section 378(4) of the CrPC (or the corresponding provision of BNSS).
If you filed a private complaint before the Magistrate for the cheque bounce (Section 138 NI Act) and a separate Police FIR/Private Complaint was registered for cheating (Section 420 IPC), resulting in two separate judgments, the appeals must follow distinct statutory routes.
Appeal against the judgment passed under section 138 NI act will lie before the district and session court. As a complainant seeking a higher punishment or an increase in the compensation/penalty amount, your remedy lies under Section 372 (Proviso) or Section 377 of the CrPC. The Supreme Court of India (Mallikarjun Kodagali v. State of Karnataka and subsequent clarifying rulings specifically extending the logic to the NI Act) has established that a complainant is the primary economic "victim" of a cheque bounce. Therefore, a victim can approach the Sessions Court directly to prefer an appeal challenging the inadequacy of the sentence or compensation awarded by a Magistrate, without requiring prior special leave.
This application asks the High Court for permission to challenge the acquittal. In the same petition, your advocate will explicitly state that you are also seeking an enhancement of the fine, compensation, and jail term for the Section 138 NI Act conviction. Once the High Court peruses the lower court records and grants "leave," the matter is officially registered as a regular Criminal Appeal and heard on its merits. If those 60 days have already passed, your advocate will need to file a separate condonation of delay application under Section 5 of the Limitation Act, showing "sufficient cause" for why the deadline was missed.