Is it prescribed to turn a shoe over and put it the right way up if the sole is facing the sky?

There is no such basis in sharee‘ah for turning over a shoe that is upside down. Ibn ‘Aqeel al-Hanbali (may Allah have mercy on him) regarded going to extremes in that regard as the one of the actions of the ignorant. He (may Allah have mercy on him) said: 

Woe to the scholar who does not strive his utmost against the ignorant …One of them swears by the Mushaf for the sake of a grain, and he strikes with the sword whomever he meets on the basis of tribal feelings. 

And they threaten the one who they see placing a loaf of bread facedown or leaving an upside-down shoe with its sole pointed towards the sky. End quote. 

Al-Adaab al-Shar‘iyyah, 1/268-269 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: 

There are some people who say that if a shoe is placed upside down, the angels will not enter that house or Allah will not look at that house. What you say about this matter? 

He replied: 

We say: That is not correct and I do not know of there being anything wrong with a shoe being upside down. But this is a very serious matter for some people. It may be very serious for some people but there is no basis for it. End quote. 

Noor ‘ala al-Darb, 13/65 

There is nothing wrong with changing the position of the shoe because the sole is usually dirty, so it is not good manners to leave it (the sole) uppermost where people can see it. 

The Standing Committee for Issuing Fatwas was asked: 

Some old people say that it is not permissible to leave a shoe upside down because it is facing towards the Face of Allah. Is this true? 

They replied: 

If a shoe is left upside down, that is off-putting and disliked, because its sole is usually in contact with the ground and the one who wears the shoe steps on the ground with it, and he may step in something dirty. End quote. 

Fataawa al-Lajnah al-Daa’imah, 26/302-303.