Though connection is common, connexion is the correct spelling. The phrase "in this connexion" (which has its proper uses) is one of the commonest forms of "padding" in official writing. In all the following examples the words should be omitted; they are doing no work.
I am directed to refer to the travelling and subsistence allowance, applicable to your Department, and in this connexion I am to say....
Mr. X is an applicant for appointment as a clerk in this Department and in this connexion I shall be glad if you will complete the attached form.
The Minister's views in general in this connexion and the nature and scope of the information which he felt would assist him in this connexion was indicated at a meeting....
On the use of the singular verb was, see Singular & Plural Verbs.
You will recollect that you anticipated despatching the material in three stages, i.e. April, May and during the first half of the present month. In this connexion I shall be glad of your confirmation that the April and May deliveries were maintained.
On this use of anticipated, see Anticipate.
It is noted that you wish to apply for . . . and in this connexion I have to advise you to contact . . .
On the use of contact, see Contact.