With the advancement of IoT edge devices, the threat to sensitive data processed at these devices is increasing. This research aims to enhance processor's built-in resilience against power analysis attacks (PAA) by expanding pipeline stages, employing diverse pipeline techniques, and integrating additional features. The paper proposes 32-bit RISC-V core micro-architectures with inbuilt cryptographic capabilities, extending the RISC-V ISA with custom AES instructions to reduce energy consumption, code size, and encryption time compared to software AES solutions. An area-efficient 128-bit, 12-clock AES based on the Masoleh S-box is integrated into the RISC-V core, resulting in low area and power overheads. Two cores are presented: Core1, a 3-stage pipelined core with a software pause, and Core2, a 4-stage pipelined core with a hardware pause for securing data with AES instructions. Despite their vulnerabilities, the integration of AES with RISC-V architecture significantly improves their intrinsic resilience against PAA. This work analyses the vulnerability and improvement in intrinsic resilience of these cores to side-channel attacks, the impact of hardware versus software pause and the effect of pipeline stages on security metrics. The proposed designs are validated on a Xilinx Basys3 FPGA and developed in UMC 65 nm technology node. Power traces generated during AES encryption are extracted using Synopsys PrimeTime PX and analyzed with a MATLAB power attack model to successfully recover all key bytes. Core1 and Core2 achieved higher throughput of 2.02x2.83x, respectively, than the Arm CryptoCell312. Core2's added circuits for hardware pause and increased number of pipeline stages significantly boost performance and enhance security against power attacks, with only a modest increase in area and power consumption.