Firstly Translation of that sentence would be "May I help you" or Can I help you ". Actually It's Interrogative form. We use questions word like क्या(what) , कैसे(how) , कहाँ (where) etc before subject to form Interrogative And to make a Question use it after subject. Example - (main kya kar sakta hoon) (What can I do). Yes it is infinitive, To help = मदद करना(Madad karna) . And in that sentence kar is conjugated with madad. तुम orआप (you) is second person, so तुम and आप is used as a subject. But word "aapka" is used as object.

aapkee is used for madad .here madad is considered as feminine gender . mean your's help . means i help you which is related to you so we use aapkee .

क्या मैं आपकी मदद कर सकता हूँ Can I help you?

क्या मैं आपकी मदद कर सकता हूँ " (1.) क्या indicates that the sentence is a yes/no question. (2.) मैं is the subject of the notional verb and a first person pronoun. (3.) आपका/आपकी/आपके is a possessive pronoun that inflects to agree with the gender, case, and number of the noun it modifies. (4.) मदद करना is the main verb of the sentence and means "help." मदद is a noun and कर is the stem form of करना. करना has been written as कर because it has been used with the modal verb सकना. (5.) सकता expresses ability and is equivalent to "can." सक is the stem. त् indicates the imperfective aspect; in other words, it indicates the action is habitual or not completed. The long आ vowel after त् indicates the gender of the verb's subject. In this sentence the gender is masculine because आ is used with the masculine gender. (6.) हूँ is the final piece of the verb phrase and shows concord with the first person pronoun मैं.