Yes, a High Court can quash an FIR even after a chargesheet has been filed. The High Court's power to do so is rooted in Section 482 of the Code of Criminal Procedure (CrPC). This power allows the High Court to prevent the abuse of legal processes and to ensure justice is served.
Elaboration:
Section 482 CrPC:
This section grants the High Court inherent powers to make such orders as may be necessary to prevent the abuse of the process of any court or to secure the ends of justice.
No Prohibition:
The filing of a chargesheet does not prevent the High Court from exercising its power to quash the FIR.
Grounds for Quashing:
The High Court can quash an FIR if it finds that the allegations, even if true, do not constitute an offense or that the continuation of the proceedings would be an abuse of the court's process.
Not a Routine Matter:
While the High Court has the power to quash, it is not a routine or automatic process. The High Court must be satisfied that there are sufficient grounds to warrant such an order.
Considerations:
In deciding whether to quash, the High Court will consider the nature and gravity of the offense, the evidence presented, and whether the continuation of the proceedings would be an abuse of the process.

Yes, a High Court can quash an F.I.R even after a chargesheet has been filed, under its inherent powers granted by Section 482 of the Criminal Procedure Code (CrPC).

Legal Position:
- The filing of a chargesheet does not bar the High Court from exercising its power under Section 482 CrPC.
- The Court can quash the FIR, chargesheet, or even the entire criminal proceedings if it finds that:
- The case is false, frivolous, or malicious.
- The allegations do not disclose a cognizable offence.
- The prosecution is an abuse of the process of law.
- The dispute is purely civil or private in nature (e.g., matrimonial settlement).
- The essential ingredients of the offence are missing.