Create a kind of quine, such that the program prints one character of itself, then two, then three and so on
Jelly, 10 bytes

“;⁾vṾÄY”vṾ


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How it works

“;⁾vṾÄY”vṾ  Main link. No arguments.

“;⁾vṾÄY”    Set the return value to the string ';⁾vṾÄY'.
         Ṿ  Uneval; yield a string representation of the string, i.e., '“;⁾vṾÄY”'.
        v   Dyadic eval; execute the string to the left, passing the string to the
            right as argument.
  ⁾vṾ         Literal; yield 'vṾ'.
 ;            Concatenate the argument ('“;⁾vṾÄY”') and 'vṾ', yielding '“;⁾vṾÄY”vṾ'.
     Ä        Accumulate; take the cumulative sum.
              Since string addition is concatenation in Python (and Jelly doesn't do
              type checks), this yields all prefixes of the string.
      Y       Join the prefixes, separated by linefeeds.