Q:

"Failed to load Project , incompatible project version" pop up appears when I open from code of xcode 9.3 in xcode 9.2

I created a project in Xcode 9.3, and When I open the same project in Xcode 9.2, it shows "incompatible project version".  
- I changed deployment target version
It asked to sign in with the team to run the project in Xcode 9.3. 
Without signing in, it shows error and does not get deployed. 

A:

If you can open the Project
You can simply change your Project Format (like the image)

Click to your Project File in xcode and change it

If you can't open the project (projectName.xcodeproj) normally
Control-click on the project file, select Show Package Contents, and then open your project.pbxproj file and make the change for:
compatibilityVersion
objectVersion

For Xcode 10.0
compatibilityVersion: "Xcode 10.0"
objectVersion :51

For Xcode 9.3:
compatibilityVersion: "Xcode 9.3"
objectVersion :50

For Xcode 8.0-9.2:
compatibilityVersion: "Xcode 8.0"
objectVersion: 48

You can find the project.pbxproj file by right clicking the .xcodeproj file in the project folder, then select Show Package Contents

A:

I edited Datasun's comment above to include correct info but here is info for other Xcode versions.  You must change both compatibilityVersion and objectVersion.  
In the project.pbx file you need to make two changes:

compatibilityVersion
objectVersion

For Xcode 9.3+:

compatibilityVersion is "Xcode 9.3"
objectVersion is 50

For Xcode 8.0-9.2:

compatibilityVersion is "Xcode 8.0"
objectVersion is 48

For Xcode 6.3-7.3.1:

compatibilityVersion is "Xcode 6.3"
objectVersion is 47

A:

Changing project format is the right way to do it.  But this requires you to be able to open the project, which is not the case.  Therefore you can manually edit project.pbxproj (you have to open *.xcodeproj to see this file) and look for compatibilityVersion:
compatibilityVersion = "Xcode 9.3";
Then you can set the required version to a lower one.  In this case it would be "Xcode 9.2", which requires you to also set the "objectVersion = 50" to 48.  This value directly correlates to the Xcode project format.    
Important: After this step you should be able to open Xcode and to change project format again from within Xcode to make sure any missing fields are updated accordingly.