Pandas- Select rows from DataFrame based on condition

I think you need boolean indexing:

df1 = df[(df['category'] == 'A') & (df['value'].between(10,20))]
print (df1)
  category  value
2        A     15
4        A     18

And then:

df2 = df[(df['category'] != 'A') & (df['value'].between(10,20))]
print (df2)
  category  value
1        B     10

Or:

df3 = df[df['category'] != 'A']
print (df3)
  category  value
1        B     10
3        B     28

EDIT: Join both conditions with | for or, dont forget add () to first conditions.

df1 = df[((df['category'] == 'A') & (df['value'].between(10,20))) | 
         (df['category'] != 'A')]
print (df1)
  category  value
1        B     10
2        A     15
3        B     28
4        A     18