High-precision light curves were extracted from TESScut images. Together with APOGEE and LAMOST medium-resolution spectra, a joint study was made for six early K-type contact binary candidates selected unbiasedly with orbital periods around 0.268 day. It is found that all of them (RV CVn, EK Com, V384 Ser, V1038 Her, EH CVn, and CSS_J125403.7+503945) are W-subtype shallow contact systems, though with different mass ratios (1/q = 0.27-0.62). The effective temperature differences between the binary components are around a few hundred kelvins. The original definitions of the A and W subtypes were compared with the customarily used methods, which rely on the shape or photometric solutions of the light curves. The latter two methods are not always reliable; therefore, the radial velocity analysis is strongly recommended. Through a collection of all available K-type contact binaries with both photometric and spectroscopic measurements, it is found that almost all of them are W-subtype systems, except for a few objects that have nearly identical temperatures for binary components. This W-subtype phenomenon for K-type contact binaries should be further checked with more samples in the future. Finally, the physical parameters of the targets were determined with joint data analysis, and the multiplicity is discussed for these targets. Objects V384 Ser and RV CVn are confirmed to very likely be triple systems from comprehensive analysis, while V1038 Her is a candidate of a triple system based on photometric and spectroscopic solutions.