Hey ajeetha210,
Thank you for using the Apple Support Communities! We understand you're running into issues updating to macOS Big Sur on your MacBook Air. We're happy to help out.
When you say the update error's out, what are you seeing exactly? Do you see either download failed, or the update is not available at this time, etc.?
Typically download issues occur due to network conditions. Have you tried downloading and installing the macOS update via a different Wi-Fi network or via an Ethernet connection? Connect your Mac to the internet
Do you have any third party firewall, VPN , or networking software that may be altering or interfering with the download? Do you have any external hard drives, audio devices, or other peripherals connected to your MacBook Air? If so, remove or disable each of those items and try again.
You can also try downloading and installing the macOS update from another user account: Set up users, guests, and groups on Mac. If that fails too, try in safe mode instead: How to use safe mode on your Mac
Best regards.