From the version 1.1.0-AC AssetIT supports linking assets to Jira issue.

You need to have Asset custom field and already configured the field on Issue Screens.

Please follow this guide to add Asset field to Jira project

For company-managed project add-additional-asset-fields

For team-managed project link-an-asset-to-a-request-in-team-managed-projects

Once you have the Asset field, you can open it from Create Issue dialog or on the right panel of the issue details screen

From Create Issue

From the Asset field, search and select one or multiple assets by names

On the right panel

Click on Link asset to open the panel, search for asset by name and add into the issue