Q. When a father makes the Pidyon Haben for his first born son does he have to have a special Kavana or intention to comply with the mitzva? How about the Cohen?

A. It is commonly known that there are three mitzvos that require an added special Kavana or intention to keep in mind when performing them, besides the complying with the basic mitzva itself.

They are: Tzitzis, as the Torah writes: “In order that you shall recall my mitzvos and do them” (Bam’. 15 : 40); Tefillin, as mentioned (Shem’. 13: 9) “In order that the Torah shall be in your mouths”, and Sucah, as written; “In order that you recall the redemption from Egypt when Hashem caused you to dwell in clouds of glory (Vayikra 23:43). Since the word “l’ma’an” – meaning ‘because’ or ‘in order that,’ the Torah explicitly indicated the purpose of the mitzva, and one must have intention not only for complying with the act of the mitzva itself but also with the reason mentioned.

Although, Derech Pekudecha (18) maintains that one does not comply with the above three mitzvos if one does not have in mind the added kavana, most Poskim disagree, and opine that although one did not abide with the mitzva properly, after the fact one complied.
P’ri Megadim (Mishbetzos Z’ 8) added to the above list also the mitzva of Pidyon Haben for a first born son.

As is written; (Shemos 13: 13); And every firstborn donkey you shall redeem with a lamb, and if you do not redeem [it], you shall decapitate it, and every firstborn of man among your sons, you shall redeem. And it will come to pass if your son asks you in the future, saying, “What is this?” you shall say to him, “With a mighty hand did Hashem take us out of Egypt, out of the house of bondage. And it came to pass when Pharaoh was too stubborn to let us out, Hashem slew every firstborn in the land of Egypt, both the firstborn of man and the firstborn of beast. Therefore, I slaughter [for a sacrifice] all males that open the womb, and every firstborn of my sons I will redeem.

Although, Shebet Halevy (6: 169) disagrees, it is certainly better to follow on the onset the opinion of the Pri Megadim.
Horav Shlomo Miller’s Shlit’a opinion is similar

Rabbi A. Bartfeld as revised by, Horav Dovid Pam, Horav Aharon Miller, Horav Chanoch Ehrentreu and Horav Kalman Ochs Shlit’a