No, a critical hit allows you roll all of the attack's damage dice twice, and then you add any relevant modifiers as normal. The protector aasimar racial ability adds a flat amount of extra damage to the damage dice being rolled. Since this extra damage isn't based on dice rolls, you do not double the amount.
If I roll a crit, do I get to double the radiant damage from the assimar racial ability?
No, a critical hit allows you roll all of the attack's damage dice twice, and then you add any relevant modifiers as normal. The protector aasimar racial ability adds a flat amount of extra damage to the damage dice being rolled. Since this extra damage isn't based on dice rolls, you do not double the amount.
Rule of thumb for crits: roll twice, add once
Thanks