With time words like 'today', 'yesterday', 'tomorrow' used as nouns, we use possessive 's' but without 'the'. 'Today's' (A) is correct. 'The today's' (B) is wrong - we don't use 'the' with these possessives. 'A today's' (C) is wrong - never use 'a'. 'This day's' (D) is incorrect form.