The issue is not Pattern.quote, but rather your use of Matcher.find:

Attempts to find the next subsequence of the input sequence that matches the pattern. This method returns true if a subsequence of the input sequence matches this Matcher object's pattern.

So Matcher.find skips non-matching data to find the next match.

Whole word matching requires you to use the word boundary matchers like \b, while whole input matching is achieved using Matcher.matches:

Attempts to match the entire region against the pattern.

The issue is not Pattern.quote, but rather your use of Matcher.find:

Attempts to find the next subsequence of the input sequence that matches the pattern. This method returns true if a subsequence of the input sequence matches this Matcher object's pattern.

So Matcher.find skips non-matching data to find the next match.

Whole word matching requires you to use the word boundary matchers like \b, while whole input matching is achieved using Matcher.matches:

Attempts to match the entire region against the pattern.

To find whole words, within the over-all input, containing certain character sequences you simply need to tweak your code thus:

String datum= 'Looking into  dataframe or DataFrame';

Pattern p = Pattern.Compile('(?i)\\b\\w*' + Pattern.quote('af') + '\\w*\\b');
Matcher m = p.matcher(datum);
while (m.find()) {
    Integer s = m.groupCount();
    for (Integer i = 0; i <= s; i++) {
        System.debug(m.group(i));
    }
}

This looks for a case-insensitive match against:

1. A word boundary
2. Followed by zero or more word class characters
3. Followed by your quoted search term
4. Followed by zero or more word class characters
5. Followed by a word boundary

The issue is not Pattern.quote, but rather your use of Matcher.find:

Attempts to find the next subsequence of the input sequence that matches the pattern. This method returns true if a subsequence of the input sequence matches this Matcher object's pattern.

So Matcher.find skips non-matching data to find the next match.

The issue is not Pattern.quote, but rather your use of Matcher.find:

Attempts to find the next subsequence of the input sequence that matches the pattern. This method returns true if a subsequence of the input sequence matches this Matcher object's pattern.

So Matcher.find skips non-matching data to find the next match.

Whole word matching requires you to use the word boundary matchers like \b, while whole input matching is achieved using Matcher.matches:

Attempts to match the entire region against the pattern.