Recent attention-based volumetric segmentation (VS) methods have achieved remarkable performance in the medical domain which focuses on modeling long-range dependencies. However, for voxel-wise prediction tasks, discriminative local features are key components for the performance of the VS models which is missing in attention-based VS methods. Aiming at resolving this issue, we deliberately incorporate the convolutional encoder branch with transformer backbone to extract local and global features in a parallel manner and aggregate them in Cross Feature Mixer Module (CFMM) for better prediction of segmentation mask. Consequently, we observe that the derived model, Y-CT-Net, achieves competitive performance on multiple medical segmentation tasks. For example, on multi-organ segmentation, Y-CT-Net achieves an 82.4% dice score, surpassing well-tuned VS Transformer/CNN-like baselines UNETR/ResNet-3D by 2.9%/1.4%. With the success of Y-CT-Net, we extend this concept with hybrid attention models, that derived Y-CH-Net model, which brings a 3% improvement in terms of HD95 score for same segmentation task. The effectiveness of both models Y-CT-Net and Y-CH-Net verifies our hypothesis and motivates us to initiate the concept of Y-CA-Net, a versatile generic architecture based upon any two encoders and a decoder backbones, to fully exploit the complementary strengths of both convolution and attention mechanisms. Based on experimental results, we argue Y-CA-Net is a key player in achieving superior results for volumetric segmentation.