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Hello,

I appreciate your clarifications, that is, in Sam's reply and in the following one.

Could you please check if the above underlined phrases in bold are grammatically correct?

What is the syntax used after 'that is' in sentence constructions? In other words, what grammatical words are required immediately after every 'that is'?

I hope to hear from you.

Thank you.

With best wishes.
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This is OK:

I appreciate your clarifications, that is, in Sam's reply and in the following one.

that is = i.e.

that is, (by way of explanation, clarification, or an example); more accurately: 'I read the book, that is, I read most of it'. Also, 'that is to say'.
Comments  
I believe "I read the book, that is, I read most of it." is incorrect. The clause "I read most of it" is not a definitive clarification that the book was read. It actually tells us the opposite. We aren't even able to infer what was read and what was not.

Also, "that is" must be able to be replaced by the phrase "in other words", and the sentence will still be correct and fluid. Doing so to this sentence would result in "I read the book, in other words I read most of it."

Instead, "that is" is being used transitionally to concede or retract the point made in the first clause and correct it with the second clause. When used in this manner the phrase is actually "that is to say".

i.e. = that is
that is = that is to say
i.e. ≠ that is to say

Transitional phrases, much like conjunctive adverbs, are used to link two independent clauses and connect closely related ideas. The connection can indicate result, concession, apposition, addition, time, contrast, summary, or reinforcement.

When punctuating a sentence using a transitional phrase, the first clause is followed by semicolon; then the transition, uncapitalized, followed by a comma; and then the second clause.

Thus, "I read the book; that is, I read most of it."

I guess I should note that the other sentence is also wrong, but only because the second clause should be written "those in Sam's reply and in the following one."