Assalam Alaikum! How can one ask forgiveness from calling Muslims Kuffaar (disbelievers)? If a Muslim committed some blasphemy, apostasy, or Kufr (disbelief), whether major or minor, how should he repent and what is the punishment for him if he returns back to Islam.
Does that differ between men and women?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Takfeer (labeling Muslims as disbelievers) is a very serious matter. There are due conditions and criteria that must be met before it is done. Taking that matter lightly and hastening to label Muslims as disbelievers without considering the due conditions and criteria is a grave and serious matter and incurs enormous corruption.

Such an act (i.e. hastily condemning Muslims as disbelievers without careful investigation) requires repentance. The due conditions of repentance in this case are the same as the well-known conditions of repentance.

Hence, this person should denounce that act and proclaim his mistake in labeling Muslims as disbelievers and endeavor to put things right and rectify the situation. This is because Allah, The Exalted, says (what means): {Except for those who repent and correct themselves and make evident [what they concealed]. Those - I will accept their repentance, and I am the Accepting of repentance, the Merciful.}[Quran 2:160]

Ibn Katheer commented on the verse, saying: “The verse relates to those (sinners) who regret what they have done and correct their behavior and, thus, explain to the people what they have been hiding (i.e. proclaim their mistake and explain their situation).”

The same applies to the repentance from apostasy when a Muslim commits the offense of blasphemy against the religion of Allah and the like. It is incumbent on the doer, who utters a blasphemous word or commits a blasphemous act, to repent from his sin. If he denied any established facts/rulings of Islam, he must proclaim his belief in them. The Hanbali scholar Al-Hajjaawi wrote, “The repentance of the apostate and whoever commits an act of disbelief that takes him out of the fold of Islam is to testify that none is worthy of worship except Allah and that Muhammad is the Messenger of Allah. Whoever denied any established facts, rulings, or obligations of Islam, must, along with saying the two testimonies of faith, proclaim his belief in what he had denied. Or he may say: ‘I denounce and disassociate myself from all that contradicts Islam.” [Zaad Al-Mustaqni’]

Whoever repents of his sins and returns to Allah in obedience, Allah accepts his repentance. A sincere repentance wipes out one's past sins; thus, a person who repents shall not be punished for such sins or subject to the Hadd (i.e. the corporal punishment determined by the Islamic Law) in this worldly life. Allah, The Exalted, says (what means): {And it is He who accepts repentance from his servants and pardons misdeeds, and He knows what you do.}[Quran 42:25]

According to the opinion of many scholars, Ta‘zeer (discretionary punishment) is waived by the sinner’s repentance. The Maaliki scholar Al-Kharshi wrote, “Ibn Al-Qaasim said: The transgressor should be subject to the discretionary punishment; however, if he repents from his transgression, Ta‘zeer is not applicable because it is waived by the repentance." [Sharh Al-Mukhtasar]

'Ulaysh said in his book Sharh Mukhtasar Khaleel, “If the sinner repents from his sin, Ta‘zeer is waived.”

However, some scholars maintained that it is permissible to subject the repentant sinner to Ta‘zeer.

Al-Fataawa Al-Kubra (authored by Ibn Taymiyyah) reads, “If the apostate’s repentance is accepted, Ta‘zeer may still be applied even after repentance.”

It should be noted that applying Ta‘zeer and punishment in these cases is the exclusive responsibility of the Muslim authority, and not the common people. In fact, the sinner is not obliged to report his sin to the Muslim authority and demand Ta‘zeer; instead, he should conceal his sins.

Finally, there is no difference between men and women in this regard.

Allah Knows best.