Magic items are a lot of fun and allow for many new options for players. It can also be one of those things that make a game memorable. However, certain classes get more attention than others. In particular, rangers and non-magic classes with magic options are left out. For this reason, I'll be looking at the Eldritch Knight specifically to provide some magic items that benefit the class.
How to Limit it?
Many items in the new addition require attunement by a particular class. This helps limit who can use the magic item and ensures that the intended class gets the benefit. Since we are making this new item, we need to consider if we will do the same. A staff is not as useful to an Eldritch Knight as a pike or longsword is. It's not very common for the normal magic classes to have access to these weapons so we can tie it to the proficiency needed for the item. There is still a chance that someone will take a feat to gain proficiency with the class of weapons. If this bothers you, you can make being an Eldritch Knight a requirement. I'd be wary of this though because the rogue also has a magic option and I wouldn't want to cut them out. At the same time, even if a wizard has the required proficiency, the item is far more useful to an Eldritch Knight as a spear if their is a weapon bonus.
An option is to provide certain bonuses to an Eldritch Knight that are not provided to other classes using the item. Most typically, this is because it adds to a class feature that the other classes don't have (extra hitpoints when using second wind, for example).
What Kind of Items?
Typically, the most common items I've seen in this case is taking a normal staff that any spellcaster could attune to or only specific ones (such as the staff of the magi) and switching it over to Eldritch Knights for attunement with a different weapon. For example, take a staff of the magi, change the attunement to Eldritch Knight and swap staff to spear. You can also take the effects of a robe or similar magic items not availible to an Elritch Knight and either make an exception, create a new item that they can use (otherwise identical), or add the property to a different item (add the properties of the robe of the archmagi to a suit of +3 plate armour). The results are potentially extremely powerful, but the items we are taking the effects from are already powerful.
There is, however, more you can do. I would recommend giving another option for the charges that helps the martial side of the class. Similar to some other items that already exist, allowing the Eldritch Knight to spend some capped number of charges (max number of 3) to do extra damage (1D6 or 1D8 per spell slot from a staff of fire, for example). Such a feature would be far less useful to normal spellcasters but extremely beneficial to the multiattack features of the Eldritch Knight. You can also, or instead, allow the user to cast a fireball centred on themselves to which they are immune at the same time as they take the attack action. Items that boost the slot level used, grant resistance against some type of damage (including spell), or allow spells that they usually would not have access to (being stuck at 4th level spells at the most) are all good contenders as well. You can also allow more uses of a particular unique class feature (extra use of action surge or second wind) but I'd be more careful about this kind of thing than the above. Applying a modifier to the second wind feature seems to be relatively safe from the games I've played while also being a significant benefit.