Parkinson's disease (PD) is a prevalent neurodegenerative disorder globally. The eye's retina is an extension of the brain and has great potential in PD screening. Recent studies have suggested that texture features extracted from retinal layers can be adopted as biomarkers for PD diagnosis under optical coherence tomography (OCT) images. Frequency domain learning techniques can enhance the feature representations of deep neural networks (DNNs) by decomposing frequency components involving rich texture features. Additionally, previous works have not exploited texture features for automated PD screening in OCT. Motivated by the above analysis, we propose a novel Adaptive Wavelet Filter (AWF) that serves as the Practical Texture Feature Amplifier to fully leverage the merits of texture features to boost the PD screening performance of DNNs with the aid of frequency domain learning. Specifically, AWF first enhances texture feature representation diversities via channel mixer, then emphasizes informative texture feature representations with the well-designed adaptive wavelet filtering token mixer. By combining the AWFs with the DNN stem, AWFNet is constructed for automated PD screening. Additionally, we introduce a novel Balanced Confidence (BC) Loss by mining the potential of sample-wise predicted probabilities of all classes and class frequency prior, to further boost the PD screening performance and trustworthiness of AWFNet. The extensive experiments manifest the superiority of our AWFNet and BC over state-of-the-art methods in terms of PD screening performance and trustworthiness.