You may use a comma after "way", but often, people don't use one. In rare cases they use a comma after "but" and one after "way". (but along the way)
You never use a comma after or before "that" when "that" is a conjunction. (This the case of the sentence in the OP.)
- The student said that he would come.
As a relative pronoun, "that" cannot be nonrestrictive, and so you never use a comma after or before "that" when it is a relative pronoun. (You always use a comma before a pronoun that is nonrestrictive, but only "who", "whom", "which" and "whose" can be nonrestrictive.)
The house that you see over there is for sale. (restrictive)
The shopkeeper, whose shop had not been open for weeks, was poor. (nonrestrictive)
Additions following comments
User Stuart, comparison with 19th century English, in Ivanhoe
Today some of these commas would not be used; for instance, in "from which it may be inferred, that it was put on by slipping it…" (Ivanhoe) no comma is used. "It seemed to be your opinion, that" (Ivanhoe) would not be written with a comma nowadays (it's their opinion that). There are nevertheless in Ivanhoe uses of the comma before "that" that are still valid, but they are the exception to the rule; they do not occur in simple constructions. "Rely on this, that…" (Ivanhoe) is still written with a comma nowadays, but that is not the plain construction. There is then the case of the introduction of adverbs; the "I am conscious, however, that the slight, unsatisfactory, and …" in Ivanhoe should today still be written in the exact same way, but this is not the plain construction. It would be an error today to write "I am conscious, that…". Introducing "first" in the "inferred" construction above makes the comma valid today (inferred, first, that); I don't think it is necessary though, it is rather optional.
User Edwin Ashworth
, alternative modern point of view
The reader might be interested in considering that the term "conjunction" used above is not considered proper in modern linguistics, in which the idea is put forward that this word is not a conjunction; the details as to the demonstration of this fact will have to sought in the literature on the subject.
(Wikipedia) In linguistics (especially generative grammar), a complementizer or complementiser (glossing abbreviation: comp) is a functional category (part of speech) that includes those words that can be used to turn a clause into the subject or object of a sentence. For example, the word "that" may be called a complementizer in English sentences like "Mary believes that it is raining". The concept of complementizers is specific to certain modern grammatical theories. In traditional grammar, such words are normally considered conjunctions. The standard abbreviation for complementizer is C.