This study introduces a novel zero-shot scan-specific self-supervised reconstruction method for magnetic resonance imaging (MRI) to reduce scan times. Conventional supervised reconstruction methods require large amounts of fully-sampled reference data, which is often impractical to obtain and can lead to artifacts by overly emphasizing learned patterns. Existing zero-shot scan-specific methods have attempted to overcome this data dependency but show limited performance due to insufficient utilization of k-space information and constraints derived from MRI forward model. To address these limitations, we introduce a framework utilizing all acquired k-space measurements for both network inputs and training targets. While this framework suffers from training instability, we resolve these challenges through three key components: an Attention-guided K-space Selective Mechanism (AKSM) that provides indirect constraints for non-sampled k-space points, Iteration-wise K-space Masking (IKM) that enhances training stability, and a robust sensitivity map estimation model utilizing cross-channel constraint that performs effectively even at high reduction factors. Experimental results on the FastMRI knee and brain datasets with reduction factors of 4 and 8 demonstrate that the proposed method achieves superior reconstruction quality and faster convergence compared to existing zero-shot scan-specific methods, making it suitable for practical clinical applications. The implementation of our proposed method is publicly available at https://github.com/joojinho97/AeSPa.git.