Directly from Apple, it says you can use the escape:
Special String Characters
The backslash (\) and double-quote (") characters have special meaning
in text. AppleScript encloses text in double-quote characters and uses
the backslash character to represent return (\r), tab (\t), and
linefeed (\n) characters (described below). So if you want to include
an actual backslash or double-quote character in a text object, you
must use the equivalent two-character sequence. As a convenience,
AppleScript also provides the text constant quote, which has the value
Table 6-1 Special characters in text Character To insert in text
Backslash character (\) \\ Double quote (") \" quote (text constant)
On that same page, Apple says you can use
quote to insert
set myString to "this is a " & quote & "quoted" & quote & " text."
Another option found is:
set inString to "quoted"
set myString to "this is a " & quoted form of inString & " text."
Edit: Though, you said that last one outputs
this is 'quoted' text.