Toss chicken with 1 1/2 tsp of the Cajun seasoning and 1/2 tsp of the salt. In a large bowl, whisk flour, beer and remaining 1 1/2 tsp Cajun seasoning and 1/2 tsp salt. Toss chicken and peppers in batter and coat completely.
In a Dutch oven, heat oil to 375 deg. Working in 3 batches, drop chicken pieces and peppers into oil, one piece at a time. Fry for 3 minutes, gently stirring halfway through cooking time.
With a slotted spoon, remove chicken and peppers from oil and place on a paper-towel-lined baking sheet. Serve immediately with, if desired, honey mustard and ranch.