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I am writing an article on "God, Types of Worship" and I'm looking for a term which describes worshiping a single god at a time.

That is, given that different gods exist, the practise of worshiping only one of these at a given time, then moving on to worship another god. The focus of worship changes, but the worshiper's overall religion remains the same.

Monotheism is not the word I am looking for. I know the term but I can't recall it.

____ is the practise of worshiping one god of many extant gods, one at a time.

The term you are looking for is Kathenotheism. It was coined by Max Muller from Greek kath' hen "one by one" i.e. kata- "according to" + en- "one" plus -theism.

So, in Kathenotheism (it is not a religion in itself, it is use to denote a particular type of religion) you worship one God head at a time and then move ahead to worship another Gods (Trinity)/Deities in same sect, or religion.

Reference from Wikipedia https://en.wikipedia.org/wiki/Kathenotheism

Müller coined the term in reference to the Vedas, where he explained each deity is treated as supreme in turn.

Please note, Kathenotheism is different from Polytheism. In Polytheism, we worship all Gods (Trinity) and other deities at the same time, but in Kathenotheism we worship ONLY one God at a time, then move ahead to worship another one.

Also, note that Kathenotheism is different from Henotheism. Henotheist person, worships only one God, and neglects all other. Henotheist, does know, that there exists other Gods and Deities, but she/he worships only ONE God. The word Henotheism was also coined by Max Muller.

I don't want to complicate things for you, but I think you should also know, the difference between Monotheism and Henotheism. Monotheism is different from Henotheism, in a way, that in Monotheism you know that there is only one God and no other i.e. no concept of Trinity or deities.

Is monolatry the word you're looking for?

Monolatry, in contrast to monotheism, refers to the worship of a single god, without denying the validity of others.

There are some good answers already offered, and I was going to jump in with monolatry myself. However I noticed that none of them actually quite meet the specifics of your question:

given that different gods exist, the practise of worshiping only one
of these at a given time, then moving on to worship another god.

• 
  Kathenotheism is somewhat similar to what you want, but doesn't actually mean you only worship one god; the kathenotheist may worship many gods, but believes only one is supreme. The ruler of the pantheon is what changes from time to time, not the object of worship.


• 
  Monolatry doesn't move on to other gods. The monolatrist believes in the existence of many gods, but worships only one.


• 
  Summodeism is another related concept; the summodeist accepts the existence of multiple gods, but believes that they are all aspects or emanations of one supreme being. He adopts different forms of worship according to which aspect he wish to appeal to, but considers them all the same being.


• 
  Henotheism is difficult because it is used in different ways by different authors. As originally defined by von Schelling, it is a synonym of monolatry. Müller (the guy who coined "kathenotheism") used it to mean something like summodeism. Edward Wente seems to make the subtle distinction that the monolatrist considers only one god suitable for worship (either because other gods are unworthy, or because of a special relationship to, say, his tribe) whereas the henotheist chooses a preferred god to worship. Either way, thought, there's no chopping and changing: once a henotheist has picked a team, he sticks with it.

So, what then is the word for believing in many gods, but worshiping one at a time? It's just polytheism. That is exactly what polytheists actually did. The Romans, for example, had 12 major gods, 12 minor gods, and hundreds of indigitamenta; the Greeks had even more. No-one can possibly worship more than, at most, one or two at a time! So if you're preparing for the harvest, you offer a sacrifice to Ceres; if it's Bacchanale time, you have a drunken orgy; if you're sick, you offer a cockerel to Asclepius.

Another word for this is henotheism, which is very similar to the already-mentioned monolatry. Both are religions where one only worships one God without denying the existence of other gods.

A less complex term might be serial monotheism; coined on the model of "serial monogamy". The reason I would prefer this term to many of the linguistically accurate offerings above is that it's immediately clear what is meant, and doesn't leave the reader floundering for a definition.