How can I decipher a date written in the form beginning ‘Jaj . . .’ in a 17th or 18th century document?

these are sometimes referred to by palaeographers as ‘Jaj dates’. The ‘Jaj’ part is a corruption of the Latin ‘i m’, meaning ‘1000’, the ‘vj’ is the Latin numeral for ‘6’, the ‘C†’ is an abbreviation of the Latin word ‘centum’ (‘one hundred’). Hence,

Jaj = 1000 vjC† = 600 and threttie twa yeiris = 32

= 1632

In image 3 the date 1663 is rendered: the year of God Jajvj C& saxti three

Jaj dates were still being written in the first decades of the eighteenth century, as image 4 shows: Jajvijc and eight yeares

Note that, in this case, the C is not capitalised and does not have a mark of abbreviation for ‘centum’.

This form of dating is easy to learn by breaking it down into component parts:

The Jaj part (= 1000)
The v, or vj, or vij part (remember that the last i is usually a j)

The abbreviation for Centum and, which might appear as ‘C† and’ or ‘C†&’ or ‘C&’ or ‘C and’
The rest of the year written longhand, usually in Scots