One option is just to use the regex | character to try to match each of the substrings in the words in your Series s (still using str.contains).

You can construct the regex by joining the words in searchfor with |:

>>> searchfor = ['og', 'at']
>>> s[s.str.contains('|'.join(searchfor))]
0    cat
1    hat
2    dog
3    fog
dtype: object

As @AndyHayden noted in the comments below, take care if your substrings have special characters such as $ and ^ which you want to match literally. These characters have specific meanings in the context of regular expressions and will affect the matching.

You can make your list of substrings safer by escaping non-alphanumeric characters with re.escape:

>>> import re
>>> matches = ['$money', 'x^y']
>>> safe_matches = [re.escape(m) for m in matches]
>>> safe_matches
['\\$money', 'x\\^y']

The strings with in this new list will match each character literally when used with str.contains.

You need to set the regex flag (to interpret your search as a regular expression):

whatIwant = df['Column_with_text'].str.contains('value1|value2|value3',
                                                 case=False, regex=True)

df['New_Column'] = np.where(whatIwant, df['Column_with_text'])

------ Edit ------

Based on the updated problem statement, here is an updated answer:

You need to define a capture group in the regular expression using parentheses and use the extract() function to return the values found within the capture group. The lower() function deals with any upper case letters

df['MatchedValues'] = df['Text'].str.lower().str.extract( '('+pattern+')', expand=False)        

For this, you will need Regular Expressions and the preg_match function.

Something like:

if(preg_match('(bad|naughty)', $data) === 1) { } 

The reason your attempt didn't work

Regular Expressions are parsed by the PHP regex engine. The problem with your syntax is that you used the || operator. This is not a regex operator, so it is counted as part of the string.

As correctly stated above, if it's counted as part of the string you're looking to match: 'bad || naughty' as a string, rather than an expression!

df=df[df.hash_tags.str.contains('cov|corona',na=False)]

na=False means nan values if present will be evaluated to false

I'd create a regular expression from the words:

Pattern pattern = Pattern.compile("(?=.*adsf)(?=.*qwer)");
if (pattern.matcher(input).find()) {
    execute();
}

For more details, see this answer: https://stackoverflow.com/a/470602/660143

To extend your current code you could use an array of target words to search for, and use a loop:

$a = 'How are you ?';

$targets = array('How', 'are');

foreach($targets as $t)
{
    if (strpos($a,$t) !== false) {
        echo 'one of the targets was found';
        break;
    }
}

Keep in mind that the use of strpos() in this way means that partial word matches can be found. For example if the target was ample in the string here is an example then a match will be found even though by definition the word ample isn't present.

For a whole word match, there is an example in the preg_match() documentation that can be expanded by adding a loop for multiple targets:

foreach($targets as $t)
{
    if (preg_match("/\b" . $t . "\b/i", $a)) {
        echo "A match was found.";
    } else {
        echo "A match was not found.";
    }
}