Title words in a column except certain words

Here is one way of doing with str.replace and passing the replacement function:

def replace(match):
    word = match.group(1)
    if word not in keep:
        return word.title()
    return word

df['title'] = df['title'].str.replace(r'(\w+)', replace)

---

   number                         title
0       1             The Start for One
1       2             Today'S World any
2       3  Today'S World vs. Yesterday.

First we create your number and title column. Then we use Series.explode to get a word per row. If the word is in keep we ignore it, else apply Series.str.title:

keep = ['for', 'any', 'a', 'vs']

# create 'number' and 'title' column
df[['number', 'title']] = df['col'].str.split(".", expand=True, n=1)
df = df.drop(columns='col')

# apply str.title if not in keep
words = df['title'].str.split().explode()
words = words.str.replace(".", "", regex=False)
words = words.mask(words.isin(keep)).str.title().fillna(words)
df['title'] = words.groupby(level=0).agg(" ".join)

Output

  number                         title
0      1             The Start for One
1      2             Today'S World any
2      3  Today'S World vs. Yesterday.