Background: This study presents a Robot-Inspired Computer-Assisted Adaptive Autism Therapy (RoboCA[supercript 3]T) focusing on improving joint attention and imitation skills of children with autism spectrum disorder (ASD). By harnessing the inherent affinity of children with ASD for robots and technology, RoboCA[superscript 3]T offers a therapeutic environment designed to maximise engagement and facilitate effective skill development. It harnesses the advantages of Robot-Assisted Therapies (RATs) by employing robot avatars and integrating them with Computer-Assisted Therapies (CATs) within a web-based solution. The integration of automatic gaze and pose detection algorithms within RoboCA[superscript 3]T addresses the challenge posed by potential human error and observation bias in assessing the child's progress, thereby ensuring accurate results. This research responds to the need for more effective, technology driven therapies for autism, filling gaps in existing methods. Objectives: The primary goal of this research is to create a robot inspired computer assisted adaptive autism therapy that maximises engagement and enhances joint attention and imitation skills. Methods: The study involves 11 ASD children with 30 sessions (divided into two halves) per module over eight months, comprising 660 experimental trials, 110 familiarizations, and 110 follow-up sessions. The joint attention module evaluates the subject's gaze pattern using WebGazer for gaze detection in response to four least-to-most robot-generated cues. The imitation module utilises robot-generated pose for comparing subjects' imitated actions using Tensorflow Lite for pose estimation. Results and Conclusions: The effectiveness of therapy was substantiated by comparing Childhood Autism Rating Scale (CARS) scores before and after intervention. Significant improvements were noted between the first and second therapy halves, validated by Wilcoxon signed-rank tests (p < 0.01) and spearman's correlation analysis, reinforcing the observed improvements in joint attention and imitation skills.