Layered nanoparticles with surface charge are explored as rheological modifiers for extrudable materials, utilizing their ability to induce electrostatic repulsion and create a house-of-cards structure. These nanoparticles provide mechanical support to the polymer matrix, resulting in increased viscosity and storage modulus. Moreover, their advantageous aspect ratio allows for shear-induced orientation and decreased viscosity during flow. In this work, we present a synthesis and liquid-based exfoliation procedure of phenylphosphonate-phosphate particles with enhanced ability to be intercalated by hydrophilic polymers. These layered nanoparticles are then tested as rheological modifiers of sodium alginate. The effective rheological modification is proved as the viscosity increases from 10 up to 10 Pa·s in steady state. Also, shear-thinning behavior is observed. The resulting nanocomposite hydrogels show potential as an extrudable bioink for 3D printing in tissue engineering and other biomedical applications, with good shape fidelity, nontoxicity, and satisfactory cell viability confirmed through encapsulation and printing of mouse fibroblasts.