Connexion is an archaic variant of the noun we now spell connection. (Similarly, reflexion, inflexion, etc. are now most often spelled with the -ction ending.) It was fairly common in British English until the late 20th century, but today the spelling has faded out of use except in a few proper nouns (usually company names) and special uses. Many if not most speakers of British English would regard it as strange or incorrect, and most usage guides advise against it, but several British-oriented dictionaries claim it remains a standard variant.
Here are a few examples of connexion used in old texts:
This uniting principle among ideas is not to be considered as an inseparable connexion. [David Hume, A Treatise on Human Nature, 1740]
He had married a meek little dancing-mistress, with a tolerable connexion. [Charles Dickens, Bleak House, 1853]
It was an unsuitable connexion, and did not produce much happiness. [Jane Austen, Emma, 1815]
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