Does the term 'dition' has any meaning by itself or where does it derive from?
It could be found for example in many English words, like edition, addition, expedition or extradition.
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As jlovegren mentions, the suffix is -ition, not -dition. In fact, this is a specific case of the more general suffix -ion. In Latin, the suffix -ion generally makes nouns of action from verbs, and most of the earlier English words with variants of this suffix came from Latin or French originally. Whether the form of the suffix was -ition, -ation, etc. depended on the characteristics of the Latin verb. Nouns with -ition, for example, tend to be those where the Latin verb had a past participal form with -it- - e.g. AUDIRE --> AUDITUM --> AUDITION; ADDERE --> ADDITUM --> ADDITION.
So, in answer to your question, -ition (or -ation, -tion, -ion etc.) doesn't have a meaning, as such. Instead it has a grammatical role, as a suffix which usually turns a verbal stem into a noun of action. It developed to perform this function with native English verbs as well as Latin ones. Examples not from Latin include FLIRT --> FLIRTATION, and STARVE --> STARVATION.
The short answer is: no. This sequence of letters comes from various roots, and it even cuts right through some of them, like -ped- below. It is not a suffix, but merely a sequence of letters. What those words do have in common etymologically is -t-ion, which is in all cases a combination of the same two suffixes -t- and -ion-.
In ex-ped-i-t-ion, it comes from Latin pes, stem ped-, meaning "foot". The original sense of the verb ex-ped-i-o was "to get the foot out of [a snare]" (-i- is here a suffix that can turn a noun into a verb). Hence it came to connote a certain sense of (increased) movement or speed. It was already used with various similar connotations in Latin: expedio also meant roughly "to expedit".
The suffix -t- is used to form a past participle out of a verbal stem.
The suffix -io(n-) is generally added to the stem of a past participle (here ex-ped-i-t-) to form a noun of action or result: the act of expediting, or the result of expediting.
In your other examples, -di-t-ion comes from the Latin verb do, verbal stem da-, past participle da-t-us/-di-t-us, participial stem da-t-/-di-t-, meaning "give". In compound words, do also means simply "put" or "set".
In an e-di-t-ion, you give out your book to the public (Dutch uit-geven, "to give out, to publish"): Latin e(x) = "out".
In ex-tra-di-t-ion, you give someone out from your own group to the other side/party: from ex-tra = "on the outside", which is short for extra parte, "on the out-side", from the adjective ex-ter = "out", stem ex-tr-, from ex and the adjectival suffix -ter/-tr-).
In ad-di-t-ion, you give or place a certain something next to something else, as in adding something to a sum: from ad = "to, at".
But there are other words where it comes from yet other stems:
In sed-i-t-ion, it comes from se(d)- = "apart, away", plus eo = "to go", present stem e-/i-, plus the participial suffix -t-: "a going away (from a group), a rebellion".
In all of the cited words the /d/ is part of the original Latin root:
edere: to edit
addere: to add
expedire: set free
tradere: to hand over
All of these can be nominalized with a suffix -itio(n) (e.g., editio (nom.), editionis (gen.) editionem (acc.))
Merriam Webster lists Dition as an obsolete middle french word from the Latin dicion or dicio, a command word related to Dominion or Rule: https://www.merriam-webster.com/dictionary/dition?utm_campaign=sd&utm_medium=serp&utm_source=jsonld.
In that case:
ex - meaning "out of" or "from" / ped - on foot / Dition - to rule or claim dominion
this expresses far better the difference in connotation the word expedition has held historically from the word expedite.