In this work, we address the challenge of adaptive pediatric Left Ventricular Ejection Fraction (LVEF) assessment. While Test-time Training (TTT) approaches show promise for this task, they suffer from two significant limitations. Existing TTT works are primarily designed for classification tasks rather than continuous value regression, and they lack mechanisms to handle the quasi-periodic nature of cardiac signals. To tackle these issues, we propose a novel \textbf{Q}uasi-\textbf{P}eriodic \textbf{A}daptive \textbf{R}egression with \textbf{T}est-time Training (Q-PART) framework. In the training stage, the proposed Quasi-Period Network decomposes the echocardiogram into periodic and aperiodic components within latent space by combining parameterized helix trajectories with Neural Controlled Differential Equations. During inference, our framework further employs a variance minimization strategy across image augmentations that simulate common quality issues in echocardiogram acquisition, along with differential adaptation rates for periodic and aperiodic components. Theoretical analysis is provided to demonstrate that our variance minimization objective effectively bounds the regression error under mild conditions. Furthermore, extensive experiments across three pediatric age groups demonstrate that Q-PART not only significantly outperforms existing approaches in pediatric LVEF prediction, but also exhibits strong clinical screening capability with high mAUROC scores (up to 0.9747) and maintains gender-fair performance across all metrics, validating its robustness and practical utility in pediatric echocardiography analysis. The relevant dataset and code will be released upon acceptance of this paper.