Your situation is unfortunately too common whereby the chin is augmented only; and creates an imbalance in the jawline; especially viewed frontally. You can complete the jawline recontouring by augmenting the 'middle and back' of the jaw. Due to you growth pattern, you need consider the entire...
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up the deficient side with fat or fillers. Fillers, depending on their composition, are useful for treating fine lines and areas of soft tissue deflation.
A sliding genioplasty requires bone contact to allow bone
healing. This need for contact can limit the amount of advancement. Two SGs are
possible, but complicated and less than ideal in result.
An alloplastic implant could easily bring the minimum
projection that you desire.