Quite a lot of members find they have 0.25ppm or so ammonia in their tap water.  I agree with the advice above - A good conditioner like Prime will help with the initial time period after a water change and a good mature biofilter will remove the 0.25ppm in a matter of hours.  If your filter is never getting ammonia down to zero then it is not fully cycled yet.
A good general habit for people with ammonia coming in via tap water is to think in terms of smaller but more frequent water changes as a replacement for the normal advice you will hear on all sorts of matters here in the forum.  When someone recommends such and so water percentage change, just think to yourself, ok, I need to maybe spit mine into a couple of smaller changes with some time in between.  This is just a general thing.  The normal guidelines that 0.25ppm ammonia is a good general safety max still hold and if your tap situation causes you to hit that for brief periods sometimes it won't be a terrible thing.
There are two large basic habits of general maintenance that we hope our beginners section provides to all who pass through here.  The are the weekly substrate-clean-water-change and the "monthly" filter maintenance habit.
The weekly substrate-clean-water-change really is weekly, typically performed each weekend, but of couse any time works as long as it is weekly.  The is a very tough thing to maintain over the years - we all understand that and we all slip with a fair frequency I'm sure but we still like to -try!  For gravel substrates a gravel-cleaning-siphon is used to disturb the gravel (right down to the bottom of the tank, but be careful of the roots on live plants.)  In your case it may be difficult to complete a thorough clean and still have the water change remain smaller because of the tap ammonia.  In that case perhaps do a more shallow clean over a wider surface are as your first clean and perhaps you can do another deeper one on only a portion of substrate at a later or next clean.  Always wipe down your interior glass (even if you don't see algae or any other problem yet) and gently clean other things.. all just prior to the gravel-clean siphon part of the work.  This way a maximum of debris will go out with the water exiting water.  Water changes are extremely important to tank maintenance because they are removing invisible mineral buildups, organics and other inorganics from the water (there are literally hundreds of things that we -don't- measure that build up in the water and NO3 is just the "canary in the coal mine" that we use as a flag to tell us we need to keep getting them out).  They also remove algae spores and the fresh tap water coming in supplies calcium, magnesium and other trace minerals needed by both fish and plants.
The regular filter maintenance habit is also extremely important and we like to suggest monthly as a starting point for beginners just to put a number on it.  But in fact there are better ways to determine the rhythm of your filter cleans:  The best is to take note of the regular nitrate(NO3) test readings that should be accumulating in your aquarium notebook (you do have an aquarium notebook with daily diary, right?  This is a basic of any good aquarist.)  Anyway, in a healthy tank we often see nitrate(NO3) levels not exceeding 15 to 20ppm -above- whatever the tap nitrate level is (eg. 15-20ppm NO3 if you have no tap nitrate, or higher if you do) Often we see even lower levels than this and sometimes we see higher - the steady state is not so important - what -is- important is to note whether they are creeping up on you over time.  That is a sign that more maintenance is needed and filter maintenance may indeed be the part that needs to get more frequent (because of course you are doing your weekly gravel routines, we assume.)
The actual steps of filter maintenance are spelled out in numerous of our documents in the Beginners Resource Center,  tank water, not tap water, should always be used in rinsing your media and cleanings should be gentle to reasonable, not overly aggressive.  You are just unclogging your media, not trying to make it "clean."  Speaking of unclogging, any time one notices reduced flow, a filter cleaning should follow.  Filters having significantly reduced flow is a serious problem as not only might the biofilter not be able to function efficiently, you might also begin to lose bacteria in a worst case.
~~waterdrop~~ (whew!  

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