There is no need for dynamic allocation here, since you do not know the length of the string in advance, so just do:
void printLetter() {
    char string[100]; // example size 100
    ...
    scanf("%99s", string); // read no more than your array can hold
}
A fun exercise would be to count the length of the string, allocate dynamically exactly as mush space as you need (+1 for the null terminator), copy string to that dynamically allocated space, use it as you wish, and then free it.
Moreover this:
printf("%c\n", string[n+1]);
should be written as this:
printf("%c\n", string[n-1]);
since you do not want to go out bounds of your array (and cause Undefined Behavior), or print two characters next of the requested character, since when I ask for the 1st character, you should print string[0], when I ask for the 2nd, you should print string[1], and so on. So you see why we need to print string[n-1], when the user asks for the n-th letter.
By the way, it's common to use a variable named i, and not n as in your case, when dealing with an index. ;)
In your code, this:
char * string = malloc(sizeof(char));
allocates memory for just one character, which is no good, since even if the string had one letter only, where would you put the null terminator? You know that strings in C should (almost) always be NULL terminated.
In order to allocate dynamically memory for a string of size N, you should do:
char * string = malloc((N + 1) * sizeof(char));
where you allocate space for N characters, plus 1 for the NULL terminator.