Do we need preposition "of" after a year?
Freud is a visitor at James’s Sussex residence, Lamb House, in the year 1908
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It's technically acceptable either way, but the preferred use is "in the year 1908". The word 'of' is used to indicate derivation, origin, or source, and it's obvious in this sentence which year is being referenced. If you're a fan of economy of langauge, you can even omit "the year" to produce a less-antiquated form of speaking:
Freud is a visitor at James's Sussex residence, Lamb House, in 1908.
(Again, it's not only obvious but assumed that you're talking about the year 1908 AD)
Question...are you quoting something or did you write that sentence? If you wrote it, consider that "Freud is..." probably should be changed to "Freud was...".
When giving the year by its date, “of” should be omitted:
George Washington was born in the year 1732.
is correct; ‘the year of 1732’ is unusual in modern usage, and I think in most historical usage too. Use of ‘the year’ is also optional here: in modern usage, ‘…in 1732’ would be more common, but ‘the year’ adds emphasis and formality; in historical usage ‘…the year 1732’ was more standard.
On the other hand, if specifying the year by an event, then ‘of’ is correct:
In the year of George Washington’s birth, the King of England was George II.
(Of course, you could also phrase this as “In the year when George Washington was born, …” or similar.)