How can one control one's intention to be purely for the sake of Allah the Almighty when reciting adhkar (remembrances) and performing prayers, knowing that Allah accepts deeds only if they are for His glorious sake?

Reciting supplications with the intention of seeking protection from Satan does not contradict sincerity (ikhlas (definition)), as it is a form of seeking refuge in Allah, and it is an act of worship. The prophets encouraged supplications by highlighting their protective power against Satan, as the Prophet (peace be upon him) said: "That you remember Allah, for its likeness is that of a man whom the enemy pursued swiftly until he came to a strong fortress and secured himself from them. Similarly, a servant cannot secure himself from Satan [except by remembering Allah]."

Likewise, his saying to one of his companions: "Say 'Qul Huwa Allahu Ahad' (Say: He is Allah, [the] One) and the two 'Mu'awwidhatayn' (Al-Falaq and An-Nas) when you enter the evening and when you enter the morning, three times, they will suffice you against everything." Observing the worldly promises when performing righteous deeds does not contradict sincerity. It is more complete to add the intention of emulating and obeying the Messenger of Allah (peace be upon him), and remembering Allah to attain what He has promised those who remember Him: {And the men who remember Allah often and the women who remember Him - Allah has prepared for them forgiveness and a great reward.}

As for performing acts of obedience solely for worldly gain, without the intention of seeking closeness to Allah, its intention is corrupt, and it is considered an act for the sake of this world. Allah the Almighty said: {Whoever desires the life of this world and its adornments - We fully repay them for their deeds therein, and they therein will not be deprived. Those are the ones for whom there is not in the Hereafter except the Fire. And lost is what they did therein, and worthless is what they used to do.} And the Prophet (peace be upon him) said: "Whoever performs a deed of the Hereafter for the sake of this world will have no share in the Hereafter." And it is polytheism (shirk (definition)) for a person to intend the worldly life with his deeds.

Prayer must be maintained out of obedience to Allah the Almighty, and thereby sincerity is achieved. There is no harm in observing the attainment of relief and desired worldly matters, because Allah has promised ease to the righteous: {And whoever fears Allah - He will make for him ease in his affair.}