Airyprime beams are known for their powerful autofocusing property, which are further enhanced by the introduction of a circular structure-circular Airyprime beam (CAPB). We derive an asymptotic expression of the CAPB in Fourier space (FS) and verify its accuracy by the numerical Fourier transform (FT) method. Through FS modulation on it, adjustable control of autofocusing property of the FS-modulated CAPB can be achieved, whose lower and upper limits can reach 8.7% reduction and 2.6 times enhancement compared to the unmodulated one. The experimental results agree well with the numerical analyses. Our findings offer promising possibilities for efficient particle trapping and enhancing free-space optical communication capabilities.