Hi @Deepu K,
Thank you for posting to Microsoft Community.
Based on your description, I understand you want to add the aliases in your Hybrid environment with Azure AD Connect.
For this you could use AD User and Computer (ADUC), find the user, double click -> attribute editor -> find "proxyAddresses" and add the address. Add to the on-prem object via ADUC and it will sync via AADConnect within 30 minutes.
However, please kindly note Microsoft do not support AADConnect syncing to 365 not having at least one Exchange Server on-prem for management.
If my answer is helpful to you, please mark it as the answer so that other users can refer to it. Thank you for your support and understanding.