The prefix in‑ ‘in, inside’ was attached at some point in Latin to both sitting verbs, sĕdēre and sīdĕre, resulting in the derived verbs īnsĭdēre and īnsīdĕre, respectively. Second conjugation Lat. īnsĭdēre meant primarily ‘to sit upon, settle on’ and, figuratively, ‘to take place, settle, be fixed, adhere’ (CTL). Its principal parts were īnsĭdĕo, īnsĭdēre, īnsēdī, ?īnsĕssus. Third conjugation Lat. īnsīdĕre was a true synonym since it also meant ‘to sit in, settle on’. Its principal parts were īnsīdō, īnsīdĕre, īnsēdī, īnsĕssus. There is little doubt that these two verbs were not clearly distinguished in Latin, at least by the classical period. Notice also how these two verbs share the same third and fourth principal parts. Actually, some sources do not give a fourth principal part, īnsĕssus, for the verb īnsĭdēre, since it doesn’t seem to be attested.
Neither one of these verbs have made it into English or Spanish and only one word derived from these verbs has. A number of words were derived from īnsĭdēre, namely īnsessĭo, īnsĕssor, īnsĕssus, and īnsidiae. The first three of these words are derived from stem īnsĕss‑ of the passive participle of either of these verbs. Late Latin īnsĕssĭo (accusative wordform: īnsĕssĭōnem) was formed with the noun suffix ‑ĭōn‑ and it meant ‘the act of sitting in’. This word was borrowed by English in the 16th century for ‘the act of sitting in a bath’ and as the equivalent of ‘hip-bath or sitz-bath’. It would seem that those meanings, and the word, are now archaic, if not obsolete.
The word īnsĕssor, formed with the agent suffix ‑ōr‑, was borrowed into English at one point with the meaning ‘one who sits in or on’, but this word obviously did not catch on. Of all the major dictionaries, only the OED mentions it, giving a single attestation, from the 19th century, and it says that the word is “rare”. In ornithology, the word insessor, in plural form, namely insessores, from the New Latin Īnsessōrēs, was the name given to an order of birds in a zoological classification scheme by Vigors in 1823, also known as the ‘The Perchers or Perching birds’ (OED). In this classification, which came before the currently accepted one by Linnaeus, the insessores was ‘an order of birds that have the feet adapted for perching including the Passeres and many others’ (WNTIU).
The only word derived from one of these verbs that has resulted in a recognizable word in the modern languages is īnsĭdĭae, a feminine, plural noun, for this noun was typically used in the plural, not in the singular form īnsĭdĭa (īn‑sĭd‑ĭ‑a). This word could mean ‘snare, trap’ and, in war, ‘an ambush, ambuscade’. Figuratively, it could also mean ‘artifice, crafty device, plot, snare’. Spanish borrowed this word in the singular form insidia [in.ˈsi.d̪i̯a], with the first attestation being from the mid-15th century. The word insidia is fancy but common in Spanish and it translates into English as act of malice, malicious deed, or malicious remark when referring to an act, or as malice, maliciousness, or deceit when referring to the act’s intent.
From the noun īnsĭdĭa, Latin derived the adjective īnsĭdĭōsus by means of the first-second declension adjective forming suffix ‑ōs‑, which meant ‘cunning, deceitful, treacherous, dangerous’ (CTL) (īn‑sĭd‑ĭ‑ōs‑us). This adjective has been borrowed by both English and Spanish resulting in the cognates Eng. insidious [ɪn.ˈsɪ.dɪ.əs] ~ Sp. insidioso/a [in.si.ˈd̪i̯o.so]. Eng. insidious is first attested in the mid-16th century and it was either borrowed directly from Latin or from a French learned word borrowed from Latin. Sp. insidioso is first attested in the late 16th century and it most likely came through French as well.
The word insidious is more common than its Spanish cognate insidioso/a. Also, although their meanings do not differ much, the use of these words are not exactly the same, though dictionaries typically present the two words as good friends (equivalent). Sp. insidioso, which is at heart an adjective but can also be a noun, means just ‘that behaves with insidia, i.e. malice and deceit’ (or someone who behaves that way) and it can be applied to plans, illnesses, and people, among other things.
English insidious has come to mean something like ‘working or spreading harmfully in a subtle or stealthy manner’ (AHD) or ‘causing harm in a way that is gradual or not easily noticed’ (MWAL). Notice the gradualness connotation and the fact that this adjective is rarely used for people but rather for illnesses or behaviors. Eng. insidious is often used in collocations such as insidious disease, insidious plan, or insidious enemy. Finally, we should mention that from the adjective insidious, a synonymous adjective was created, in English, in the 17th century, namely insidiary, formed with the Latinate suffix ‑ary. This word was very rare then and is obsolete now.
Finally, we should mention that from the noun īnsĭdĭae, Latin developed a verb īnsĭdĭāre or īnsĭdĭārī ‘that meant ‘to lie in waiting, lie in ambush’ and, figuratively ‘to watch for, plot against, seize stealthily’ (CTL). The principal parts of first conjugation īnsĭdĭāre were īnsĭdĭō, īnsĭdĭāre, īnsĭdĭāvī, īnsĭdĭātum, and the principal parts of first conjugation deponent īnsĭdĭārī were īnsĭdĭor, īnsĭdĭārī, and (perfect active) īnsĭdĭātus sum. These verbs have been borrowed by both English and Spanish at different points, though they were always very rare and can probably be said to be obsolete now. English borrowed the verb insidate in the 17th century and the OED does not mention any more recent uses. Spanish also borrowed the verb insidiar, which means ‘to set traps to attract a person to an unfavorable situation’ (GDLEL). This verb is quite rare, however, and dictionaries give it as a synonym of patrimonial asechar, which is more common.
Two words related to this verb have been use English in the past, namely the noun insidiator, meaning ‘a lier in wait; a plotter’ (OED) and the noun insidiation, meaning ‘the action of lying in wait or plotting; a plot; an insidious act’ (OED). Both of these words are now considered to be obsolete.
 Sp. asechar comes from the Latin first conjugation deponent verb assectārī, which meant ‘to attend one with zeal, eagerness, etc., to accompany, follow, wait upon, be in attendance upon’ and, in legal terminology, ‘to follow a woman (considered as a wrong)’ (L&S). Its principal parts were assector, assectārī, assectātus sum. This verb was formed from by addition of the prefix ad‑ ‘to, towards, at’ to the deponent verb sectārī ‘to follow continually, attend, accompany’, derived from the also deponent verb sequī ‘to follow’, whose principal parts were sequor, sequī, secūtus sum (cf. Sp. seguir).