By attaching the prefix dĭs‑, to the verb sĕdēre, the derived verb dĭssĭdēre was formed in Latin. (Note that here too the derived verb has the sĭd‑ allomorph of the sĕd‑ morpheme.) The prefix’s meaning in this context was ‘asunder, apart, in two’ (other meanings of the prefix dĭs‑ are ‘reversal, removal’ and ‘utterly, exceedingly’ (intensifier). Thus, the main meaning of the verb dĭssĭdēre was ‘to sit apart’ and, derived from it, ‘to be remote from, to be divided, separated’ (L&S). A secondary, derived, figurative meaning was ‘to be at variance, disagree, differ’ (CTL). The verb’s principal parts were (present indicative) dĭssĭdĕō, (present infinitive) dĭssĭdēre, and (perfect active) dĭssēdī (this verb had no supine or passive participle forms).
Excursus: Lat. dĭssĕntīre
A partial synonym of the English noun dissidence is dissent, which is both a noun and a verb. The verb to dissent (from), which came first, means ‘express disagreement with a prevailing view or official decision’ (COED) and the noun dissent, which is derived by conversion (zero-derivation) from the verb, means ‘the holding or expression of a dissenting view’ (COED). However, the words dissidence and dissent are not related to each other except that in both cases the Latin source word contains the same prefix dĭs‑.