If I click the back button in an assignment then skips the field level validations and move to back step, If I click the submit button in same assignment it follows field level validations and doesn't finish assignment. (It should be the process flow).
Hope you need to go back from an assignment to the previous one as given in the flow on click of the back button, and should validate and process the assignment on click of the submit.
If this is the requirement, The best practice is to use a screen flow.
I you want to proceed with the process flow, use customized buttons one which calls the finish assignment without the validations (Obj-validate) moves to the next; and the other which finishes the assignments with all validations. You can set some property on click of each button to get differentiated between the buttons. In the post action do actions based on the button which is clicked.