In this work, squaric acid (3,4-dihydroxycyclobut-3-ene-1,2-dione) was used as a coformer to pyridine carboxylic acid cocrystallization. Among three newly prepared complexes are an example of a salt–cocrystal continuum – pyridinium-2-carboxylate squaric acid adduct (1) and two ionic complexes – pyridinium-3-carboxylic acid hydrogen squarate hemihydrate (2), and pyridinium-4-carboxylic acid hydrogen squarate (3). X-ray structural analysis showed that picolinic acid exists in 1 as a zwitterion. In turn, pyridine carboxylic acids in 2 and 3 are in a cationic form. In the structures optimized at the APF-D/6-311++G(d,p) level of theory, no proton migration between the acid molecules is observed (molecular complex, or cocrystal), while single-crystal X-ray diffraction studies showed that proton transfer takes place and the obtained systems are called the hydrogen-bonded ion pair. The frontier molecular orbitals (HOMO and LUMO) were also analyzed. The global reactivity parameters (chemical potential, global hardness, global softness, global electrophilicity index, and maximum charge transfer index) were considered. The experimental and computed infrared spectra were compared. Additionally, the high thermal stability of novel squaric acid complexes was confirmed by thermogravimetric and differential scanning calorimetry methods. The preliminary studies on the fungistatic activity showed inhibiting properties against Poria placenta.