How to publish artifacts separately for each project in solution from VSTS CI pipeline?

You can use multiple, Publish tasks to create multiple artifacts in a single build definition.

For example lets say, you have below, as your current artifacts for a single project, comprising of _PublishedWebsites\MVS5WebApp (XCopy deployable website) and _PublishedWebsites\MVS5WebApp_Package (web deploy package).

If you want to separate these two, into two artifacts, you can use two Publish Artifact tasks as shown below, each one specifying exact path to publish (this path does not support wildcards, you just have to specify the folder you need to publish)

This will give you output as shown below.

In this example I just only used the Publish Artifacts task and created two artifacts using a single web site project. You can do same for your two project scenario. If you want to use wild card to filter more files before publish you can use "Copy File" task multiple times as required.

If you are using '.net core' task in the build pipeline then uncheck the checkbox 'Publish web projects' just after the command textbox.

Then it automatically creates publish artifacts separate for each project in the solution with the same name as each of the project files.