The physical mechanisms supporting the existence of topological interface modes in photonic structures, formed with the concatenation of two finite, N-period, one-dimensional photonic crystals, are investigated. It is shown that these mechanisms originate from a specific configuration of bands and bandgaps of topological origin in the band structure of the concatenated structure. Our analysis reveals that the characteristics of such a configuration depend on the structural parameters, including the number, N, of unit cells, and determine the properties of the corresponding resonant transmission peak. It was shown that the width and maximum value of the transmission peaks decrease with N. These results not only provide new physical insight into the origin and nature of such modes, but also can be used to control and manipulate the transmission peak properties, such as peak values, full width at half maximum (FWHM), and Q-factor, which are of special interest in the fields of optical sensing, filters, etc.